ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_fftnr::getFFTR Interface Reference

Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter. More...

Detailed Description

Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind parameter.

See the documentation of pm_fftnr for more details.

Parameters
[in]data: The input contiguous vector of arbitrary size of,
  1. type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
  2. type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),
containing the periodic sequence whose FFT is to be computed.
Returns
fft : The output vector of size getExpNext(size(data), 2) of the same type and kind as the input data, containing the FFT result.


Possible calling interfaces ⛓

use pm_fftnr, only: getFFTR
type_of(data) :: fft(1 : getExpNext(size(data)))
fft(:) = getFFTR(data(:))
pm_fftnr::getFFTR
Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type compl...
Definition: pm_fftnr.F90:611
pm_fftnr
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftnr.F90:184
Warning
The condition 1 < size(data) must hold for the corresponding input arguments.
This condition is verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.
Remarks
The procedures under discussion are impure.
Note
This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTR.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.
See also
getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI


Example usage ⛓

1program example
2
3 use pm_kind, only: SK, IK, LK
4 use pm_io, only: display_type
5 use pm_fftnr, only: getFFTF, getFFTR
6 use pm_distUnif, only: getUnifRand
7 use pm_mathCompare, only: isClose
8 use pm_err, only: setAsserted
9
10 implicit none
11
12 integer(IK) :: i
13 integer(IK) :: lenData
14 type(display_type) :: disp
15 disp = display_type(file = "main.out.F90")
16
17 do i = 1, 5
18 block
19 use pm_kind, only: TKG => CKS
20 real(TKG) :: reltol
21 complex(TKG), allocatable :: data(:), atad(:)
22 call disp%show("lenData = getUnifRand(5, 100)")
23 lenData = getUnifRand(5, 100)
24 call disp%show("lenData")
25 call disp%show( lenData )
26 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")
27 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
28 call disp%show("data")
29 call disp%show( data )
30 call disp%skip()
31 call disp%show("atad = getFFTR(getFFTF(data))")
32 atad = getFFTR(getFFTF(data))
33 call disp%show("atad = atad / size(atad)")
34 atad = atad / size(atad)
35 call disp%show("atad")
36 call disp%show( atad )
37 call disp%show("reltol = sqrt(epsilon(1._TKG))")
38 reltol = sqrt(epsilon(1._TKG))
39 call disp%show("reltol")
40 call disp%show( reltol )
41 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")
42 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )
43 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")
44 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
45 call disp%skip()
46 end block
47
48 block
49 use pm_kind, only: TKG => CKD
50 real(TKG) :: reltol
51 complex(TKG), allocatable :: data(:), atad(:)
52 call disp%show("lenData = getUnifRand(5, 100)")
53 lenData = getUnifRand(5, 100)
54 call disp%show("lenData")
55 call disp%show( lenData )
56 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")
57 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
58 call disp%show("data")
59 call disp%show( data )
60 call disp%skip()
61 call disp%show("atad = getFFTR(getFFTF(data))")
62 atad = getFFTR(getFFTF(data))
63 call disp%show("atad = atad / size(atad)")
64 atad = atad / size(atad)
65 call disp%show("atad")
66 call disp%show( atad )
67 call disp%show("reltol = sqrt(epsilon(1._TKG))")
68 reltol = sqrt(epsilon(1._TKG))
69 call disp%show("reltol")
70 call disp%show( reltol )
71 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")
72 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )
73 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")
74 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
75 call disp%skip()
76 end block
77
78 block
79 use pm_kind, only: TKG => CKH
80 real(TKG) :: reltol
81 complex(TKG), allocatable :: data(:), atad(:)
82 call disp%show("lenData = getUnifRand(5, 100)")
83 lenData = getUnifRand(5, 100)
84 call disp%show("lenData")
85 call disp%show( lenData )
86 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")
87 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
88 call disp%show("data")
89 call disp%show( data )
90 call disp%skip()
91 call disp%show("atad = getFFTR(getFFTF(data))")
92 atad = getFFTR(getFFTF(data))
93 call disp%show("atad = atad / size(atad)")
94 atad = atad / size(atad)
95 call disp%show("atad")
96 call disp%show( atad )
97 call disp%show("reltol = sqrt(epsilon(1._TKG))")
98 reltol = sqrt(epsilon(1._TKG))
99 call disp%show("reltol")
100 call disp%show( reltol )
101 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")
102 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )
103 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")
104 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
105 call disp%skip()
106 end block
107
108 block
109 use pm_kind, only: TKG => RKS
110 real(TKG) :: reltol
111 real(TKG), allocatable :: data(:), atad(:)
112 call disp%show("lenData = getUnifRand(5, 100)")
113 lenData = getUnifRand(5, 100)
114 call disp%show("lenData")
115 call disp%show( lenData )
116 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")
117 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
118 call disp%show("data")
119 call disp%show( data )
120 call disp%skip()
121 call disp%show("atad = getFFTR(getFFTF(data))")
122 atad = getFFTR(getFFTF(data))
123 call disp%show("atad = atad * 2 / size(atad)")
124 atad = atad * 2 / size(atad)
125 call disp%show("atad")
126 call disp%show( atad )
127 call disp%show("reltol = sqrt(epsilon(1._TKG))")
128 reltol = sqrt(epsilon(1._TKG))
129 call disp%show("reltol")
130 call disp%show( reltol )
131 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")
132 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )
133 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")
134 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
135 call disp%skip()
136 end block
137
138 block
139 use pm_kind, only: TKG => RKD
140 real(TKG) :: reltol
141 real(TKG), allocatable :: data(:), atad(:)
142 call disp%show("lenData = getUnifRand(5, 100)")
143 lenData = getUnifRand(5, 100)
144 call disp%show("lenData")
145 call disp%show( lenData )
146 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")
147 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
148 call disp%show("data")
149 call disp%show( data )
150 call disp%skip()
151 call disp%show("atad = getFFTR(getFFTF(data))")
152 atad = getFFTR(getFFTF(data))
153 call disp%show("atad = atad * 2 / size(atad)")
154 atad = atad * 2 / size(atad)
155 call disp%show("atad")
156 call disp%show( atad )
157 call disp%show("reltol = sqrt(epsilon(1._TKG))")
158 reltol = sqrt(epsilon(1._TKG))
159 call disp%show("reltol")
160 call disp%show( reltol )
161 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")
162 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )
163 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")
164 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
165 call disp%skip()
166 end block
167
168 block
169 use pm_kind, only: TKG => RKH
170 real(TKG) :: reltol
171 real(TKG), allocatable :: data(:), atad(:)
172 call disp%show("lenData = getUnifRand(5, 100)")
173 lenData = getUnifRand(5, 100)
174 call disp%show("lenData")
175 call disp%show( lenData )
176 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")
177 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
178 call disp%show("data")
179 call disp%show( data )
180 call disp%skip()
181 call disp%show("atad = getFFTR(getFFTF(data))")
182 atad = getFFTR(getFFTF(data))
183 call disp%show("atad = atad * 2 / size(atad)")
184 atad = atad * 2 / size(atad)
185 call disp%show("atad")
186 call disp%show( atad )
187 call disp%show("reltol = sqrt(epsilon(1._TKG))")
188 reltol = sqrt(epsilon(1._TKG))
189 call disp%show("reltol")
190 call disp%show( reltol )
191 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")
192 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )
193 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")
194 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
195 call disp%skip()
196 end block
197 end do
198
199end program example
pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150
pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735
pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618
pm_fftnr::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftnr.F90:250
pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508
pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:535
pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274
pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52
pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252
pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393
pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268
pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541
pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:843
pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:570
pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540
pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:571
pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568
pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539
pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858
pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567
pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205
pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh
2rm main.exe
3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe
2set PATH=..\..\..\lib;%PATH%
3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh
2rm main.exe
3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)
2lenData
3+60
4data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
5data
6(+1.60516763, +0.602451324), (+1.63983965, +0.636269629), (+1.29111624, +0.499731541), (+1.85776448, +0.150928855), (+1.63146591, +0.405267835), (+1.64929247, +0.459882319), (+1.53427231, +0.644490957), (+1.30263817, +0.964613974), (+1.67436230, +0.374835432), (+1.33517003, +0.791720033), (+1.80358303, +0.430503666), (+1.27250099, +0.722164035), (+1.42060661, +0.636848927), (+1.66247416, +0.666207194), (+1.33268476, +0.621470213), (+1.12766623, +0.570049047), (+1.74153972, +0.729727685), (+1.23043489, +0.255902171), (+1.69456792, +0.160854638), (+1.24988973, +0.663878262), (+1.87187123, +0.559675097E-1), (+1.31292200, +0.836308360), (+1.59729552, +0.977720439), (+1.42257333, +0.545332849), (+1.52264762, +0.255466819), (+1.41379428, +0.287603557), (+1.28405857, +0.734730363E-1), (+1.17708087, +0.141437769), (+1.13905799, +0.842135489), (+1.11677718, +0.569504857), (+1.57381701, +0.610295475), (+1.17541587, +0.529016972), (+1.82111907, +0.491064727), (+1.61576605, +0.915351331), (+1.86341023, +0.734603882), (+1.64366829, +0.958257318E-1), (+1.66710353, +0.476203084), (+1.51723397, +0.560474515), (+1.73436832, +0.125214219), (+1.29875600, +0.541824520), (+1.47520518, +0.714543581), (+1.32089019, +0.272365391), (+1.26754475, +0.837800205), (+1.22723985, +0.458860040), (+1.19689083, +0.786947846), (+1.90134609, +0.566890836), (+1.58401036, +0.585502923), (+1.04614186, +0.528022110), (+1.63717699, +0.955838919), (+1.40691185, +0.711054921), (+1.71090531, +0.398185313), (+1.51966345, +0.225375652), (+1.36954331, +0.135884881E-1), (+1.46540499, +0.275858402), (+1.60867345, +0.960028172), (+1.30039978, +0.804669976), (+1.00407577, +0.311503530), (+1.36262894, +0.376272619), (+1.25306702, +0.506772578), (+1.24675524, +0.722192109)
7
8atad = getFFTR(getFFTF(data))
9atad = atad / size(atad)
10atad
11(+1.60516787, +0.602451324), (+1.63983953, +0.636269569), (+1.29111600, +0.499731600), (+1.85776424, +0.150928795), (+1.63146591, +0.405267745), (+1.64929223, +0.459882289), (+1.53427231, +0.644490838), (+1.30263817, +0.964613676), (+1.67436254, +0.374835521), (+1.33517003, +0.791719854), (+1.80358279, +0.430503726), (+1.27250087, +0.722163856), (+1.42060673, +0.636849105), (+1.66247416, +0.666207314), (+1.33268476, +0.621470273), (+1.12766623, +0.570049047), (+1.74153984, +0.729727685), (+1.23043478, +0.255902112), (+1.69456768, +0.160854578), (+1.24988961, +0.663878262), (+1.87187135, +0.559675395E-1), (+1.31292188, +0.836308241), (+1.59729540, +0.977720320), (+1.42257321, +0.545332789), (+1.52264762, +0.255466908), (+1.41379440, +0.287603498), (+1.28405845, +0.734731555E-1), (+1.17708087, +0.141437858), (+1.13905799, +0.842135549), (+1.11677694, +0.569504738), (+1.57381678, +0.610295534), (+1.17541552, +0.529016972), (+1.82111931, +0.491064787), (+1.61576593, +0.915351272), (+1.86341023, +0.734603822), (+1.64366817, +0.958256349E-1), (+1.66710353, +0.476203114), (+1.51723385, +0.560474455), (+1.73436821, +0.125214100), (+1.29875600, +0.541824341), (+1.47520530, +0.714543581), (+1.32089019, +0.272365391), (+1.26754463, +0.837800145), (+1.22723973, +0.458859980), (+1.19689071, +0.786947787), (+1.90134597, +0.566890955), (+1.58401036, +0.585502803), (+1.04614162, +0.528022051), (+1.63717711, +0.955838978), (+1.40691173, +0.711054862), (+1.71090508, +0.398185253), (+1.51966310, +0.225375593), (+1.36954343, +0.135884583E-1), (+1.46540487, +0.275858313), (+1.60867345, +0.960028231), (+1.30039966, +0.804669738), (+1.00407600, +0.311503500), (+1.36262906, +0.376272559), (+1.25306714, +0.506772578), (+1.24675536, +0.722191930), (+0.476837158E-6, -0.894069672E-7), (+0.178813934E-6, -0.178813934E-6), (+0.596046448E-7, +0.00000000), (+0.178813934E-6, +0.119209290E-6)
12reltol = sqrt(epsilon(1._TKG))
13reltol
14+0.345266977E-3
15isClose(data, atad(1:size(data)), reltol = reltol)
16T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
17call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
18
19lenData = getUnifRand(5, 100)
20lenData
21+33
22data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
23data
24(+1.5045035600898904, +0.41934071957593466E-1), (+1.3327514099759474, +0.73064805710249980E-1), (+1.5117303788236012, +0.68642162808090879E-1), (+1.0822487086560106, +0.56446772820512803E-1), (+1.3867342690951114, +0.93903589664372078), (+1.6221645813194874, +0.98179900558957978), (+1.9052335855191105, +0.20039337358262921), (+1.1837731070923676, +0.28918940073373967), (+1.4185249907084727, +0.61787008903254281), (+1.6797460717910493, +0.52753787896915960), (+1.0657940867693014, +0.65837413029210168), (+1.6979563391231758, +0.56403940726739565), (+1.6395190332852057, +0.43863765062950855), (+1.1220643412514391, +0.72893714796139242), (+1.0142469771765898, +0.87359155608592309), (+1.3376332076440085, +0.33596112214536078), (+1.5224406753862565, +0.16915660046111669E-1), (+1.9178087053497128, +0.24239760578964620), (+1.5481339690610429, +0.41801539693031364), (+1.2442943317070330, +0.93591762645515830), (+1.2784935895320340, +0.76025477996892743E-1), (+1.9498082696241612, +0.11617803735882526), (+1.4805639373960684, +0.15534516795307862), (+1.4262259448998305, +0.44801708043519550), (+1.3606887319456735, +0.54091610844799742E-2), (+1.2756641409081648, +0.62831067973844512), (+1.7038351667258749, +0.51563622320023805), (+1.5758321718679209, +0.33705408232173750), (+1.9721501980766827, +0.11560421874801352), (+1.3912581238954416, +0.34720843700238524), (+1.6101225715647414, +0.30277027512861265), (+1.8578274283622709, +0.46519918779167724E-1), (+1.8756605390314003, +0.94069970954713955)
25
26atad = getFFTR(getFFTF(data))
27atad = atad / size(atad)
28atad
29(+1.5045035600898899, +0.41934071957593411E-1), (+1.3327514099759474, +0.73064805710250286E-1), (+1.5117303788236010, +0.68642162808091101E-1), (+1.0822487086560106, +0.56446772820513413E-1), (+1.3867342690951110, +0.93903589664372078), (+1.6221645813194874, +0.98179900558958022), (+1.9052335855191100, +0.20039337358262918), (+1.1837731070923678, +0.28918940073373989), (+1.4185249907084727, +0.61787008903254281), (+1.6797460717910493, +0.52753787896915993), (+1.0657940867693014, +0.65837413029210168), (+1.6979563391231751, +0.56403940726739576), (+1.6395190332852052, +0.43863765062950871), (+1.1220643412514391, +0.72893714796139264), (+1.0142469771765901, +0.87359155608592309), (+1.3376332076440083, +0.33596112214536067), (+1.5224406753862563, +0.16915660046111447E-1), (+1.9178087053497128, +0.24239760578964614), (+1.5481339690610429, +0.41801539693031342), (+1.2442943317070330, +0.93591762645515808), (+1.2784935895320337, +0.76025477996892715E-1), (+1.9498082696241614, +0.11617803735882518), (+1.4805639373960680, +0.15534516795307823), (+1.4262259448998305, +0.44801708043519539), (+1.3606887319456735, +0.54091610844799465E-2), (+1.2756641409081648, +0.62831067973844479), (+1.7038351667258747, +0.51563622320023750), (+1.5758321718679205, +0.33705408232173706), (+1.9721501980766822, +0.11560421874801324), (+1.3912581238954411, +0.34720843700238491), (+1.6101225715647411, +0.30277027512861210), (+1.8578274283622704, +0.46519918779167349E-1), (+1.8756605390314001, +0.94069970954713944), (+0.0000000000000000, -0.31225022567582528E-15), (+0.33306690738754696E-15, -0.55511151231257827E-16), (+0.0000000000000000, -0.55511151231257827E-15), (-0.22204460492503131E-15, -0.11102230246251565E-15), (-0.33306690738754696E-15, -0.22204460492503131E-15), (+0.22204460492503131E-15, -0.13877787807814457E-15), (+0.0000000000000000, -0.11102230246251565E-15), (-0.11102230246251565E-15, -0.16653345369377348E-15), (+0.0000000000000000, -0.11102230246251565E-15), (+0.22204460492503131E-15, -0.33306690738754696E-15), (+0.22204460492503131E-15, -0.27755575615628914E-15), (+0.11102230246251565E-15, -0.27755575615628914E-15), (-0.11102230246251565E-15, -0.16653345369377348E-15), (+0.22204460492503131E-15, +0.0000000000000000), (+0.44408920985006262E-15, -0.11102230246251565E-15), (+0.0000000000000000, +0.22204460492503131E-15), (-0.11102230246251565E-15, +0.15265566588595902E-15), (+0.22204460492503131E-15, +0.24980018054066022E-15), (+0.0000000000000000, -0.55511151231257827E-16), (-0.22204460492503131E-15, +0.27755575615628914E-16), (+0.0000000000000000, +0.27755575615628914E-16), (+0.11102230246251565E-15, +0.49960036108132044E-15), (+0.44408920985006262E-15, +0.22204460492503131E-15), (-0.11102230246251565E-15, +0.19428902930940239E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.55511151231257827E-15), (+0.55511151231257827E-15, +0.52735593669694936E-15), (+0.33306690738754696E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.55511151231257827E-15), (+0.22204460492503131E-15, +0.72164496600635175E-15), (+0.77715611723760958E-15, +0.51347814888913490E-15)
30reltol = sqrt(epsilon(1._TKG))
31reltol
32+0.14901161193847656E-7
33isClose(data, atad(1:size(data)), reltol = reltol)
34T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
35call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
36
37lenData = getUnifRand(5, 100)
38lenData
39+69
40data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
41data
42(+1.53965086836709003661292314897405904, +0.279753550921871817661859735576435015), (+1.24290763760680684102585096938007308, +0.922303461303284093445685963068361770), (+1.61306221264484446279101976347068651, +0.441376627661753572495558267936752987), (+1.66120578401655067235979787154213600, +0.900140975799782720802553039233084196), (+1.54261690149577674975837447223109465, +0.883732852343728814613769858145685395), (+1.29240711032499226511325580125402014, +0.327475833927751796558960492862108617), (+1.72226287733388577054439839475632120, +0.583432101243137527388229095977697763), (+1.21912658718586600005447775568110797, +0.396787434089763641745514152346927405E-1), (+1.65420279493636359357433629618042047, +0.606959524030077093472452478044909949), (+1.20501535366343077535344315014070086, +0.120636575610014144927189583577048609), (+1.74571806943784261688238530668434481, +0.721750280582129678273795422698369095E-1), (+1.44071652123326506132009791065730816, +0.182929195605050821784433174368403668), (+1.37365370427358301925857046310926727, +0.287505249221206236264159852190034785), (+1.37755894410155497493565966348731854, +0.505133614991971215409525739307001179), (+1.92001897999874835566374957313241883, +0.731559105034502626520457742817443200), (+1.39877208232034276751263660774043273, +0.840363165656305232112039177947487894E-1), (+1.30710151919468455405645207080519604, +0.659487758305308459206112023398798480), (+1.81000853127440438262481841712509711, +0.459689872041245481567002363444625114E-1), (+1.92284762204827375957718580445372152, +0.993491876616609374620878502581953847), (+1.71445566021842371137544857617528621, +0.220053175724768082404437248620815294), (+1.66556962827994571740039511918532901, +0.557841567127051965036476427025552886), (+1.90428257290538728836706113859293923, +0.214325528461530136339519974570900773), (+1.99683269494690199604470150226932069, +0.262749953138453173664024363812304321), 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(+1.27275587289749317787703120956886767, +0.138818827069145001714842095670517101), (+1.09623822298391688983024355708555494, +0.259494598153438326803344482346985738), (+1.41163111633255907217366621916573292, +0.846189023865893370012346806509785382E-1), (+1.81175063406006025798629696669904815, +0.198147512436944352132605261943755506), (+1.27900892200335850495391322394426212, +0.412108159116531576030711021778862230), (+1.06838537792340299747284294529584698, +0.239707936820404816608332258455099719), (+1.07247885854591088009662618391423426, +0.793966032670005374787656201695448335), (+1.25793374179986807269803262505610375, +0.511056860205748158344838403615054152), (+1.04780549230332960709070839755299533, +0.510863120161148778738731799208728523E-1), (+1.54332815858533070915353475776657568, +0.890051408408628164589947254793404224)
43
44atad = getFFTR(getFFTF(data))
45atad = atad / size(atad)
46atad
47(+1.53965086836709003661292314897405904, +0.279753550921871817661859735576434823), (+1.24290763760680684102585096938007327, +0.922303461303284093445685963068361578), (+1.61306221264484446279101976347068632, +0.441376627661753572495558267936752891), (+1.66120578401655067235979787154213639, +0.900140975799782720802553039233084100), (+1.54261690149577674975837447223109465, +0.883732852343728814613769858145685299), (+1.29240711032499226511325580125401994, +0.327475833927751796558960492862108183), (+1.72226287733388577054439839475632120, +0.583432101243137527388229095977697666), (+1.21912658718586600005447775568110797, +0.396787434089763641745514152346924275E-1), (+1.65420279493636359357433629618042066, +0.606959524030077093472452478044909853), (+1.20501535366343077535344315014070144, +0.120636575610014144927189583577048344), (+1.74571806943784261688238530668434500, +0.721750280582129678273795422698370298E-1), (+1.44071652123326506132009791065730855, 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+0.962964972193617926527988971292463659E-34), (+0.962964972193617926527988971292463659E-34, +0.168518870133883137142398069976181140E-33), (-0.385185988877447170611195588516985464E-33, +0.192592994438723585305597794258492732E-33), (-0.577778983316170755916793382775478196E-33, +0.120370621524202240815998621411557957E-33), (-0.385185988877447170611195588516985464E-33, +0.120370621524202240815998621411557957E-33), (-0.288889491658085377958396691387739098E-33, +0.216667118743564033468797518540804323E-33), (-0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.288889491658085377958396691387739098E-33), (-0.577778983316170755916793382775478196E-33, +0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, +0.252778305200824705713597104964271711E-33), (+0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.168518870133883137142398069976181140E-33), (-0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34), (-0.385185988877447170611195588516985464E-33, +0.409260113182287618774395312799297055E-33), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, +0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.120370621524202240815998621411557957E-33), (-0.385185988877447170611195588516985464E-33, -0.601853107621011204079993107057789787E-34), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.361111864572606722447995864234673872E-34), (-0.288889491658085377958396691387739098E-33, +0.842594350669415685711990349880905702E-34), (+0.192592994438723585305597794258492732E-33, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, -0.361111864572606722447995864234673872E-34), (-0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34), (-0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33), (+0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (-0.385185988877447170611195588516985464E-33, -0.433334237487128066937595037081608647E-33), (-0.192592994438723585305597794258492732E-33, -0.722223729145213444895991728469347744E-33), (+0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33), (-0.962964972193617926527988971292463659E-34, -0.264815367353244929795196967105427506E-33), (-0.385185988877447170611195588516985464E-33, -0.481482486096808963263994485646231830E-34), (-0.770371977754894341222391177033970927E-33, -0.288889491658085377958396691387739098E-33), (-0.577778983316170755916793382775478196E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.842594350669415685711990349880905702E-34), (-0.962964972193617926527988971292463659E-34, +0.361111864572606722447995864234673872E-34), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.481482486096808963263994485646231830E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.120370621524202240815998621411557957E-33), (-0.577778983316170755916793382775478196E-33, +0.962964972193617926527988971292463659E-34), (-0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33), (-0.481482486096808963263994485646231830E-33, +0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.192592994438723585305597794258492732E-33, -0.409260113182287618774395312799297055E-33), (+0.00000000000000000000000000000000000, -0.469445423944388739182394623505076034E-33), (-0.962964972193617926527988971292463659E-34, -0.433334237487128066937595037081608647E-33), (-0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33), (-0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33), (-0.577778983316170755916793382775478196E-33, -0.698149604840372996732792004187036153E-33), (-0.481482486096808963263994485646231830E-33, -0.457408361791968515100794761363920238E-33), (-0.385185988877447170611195588516985464E-33, -0.433334237487128066937595037081608647E-33)
48reltol = sqrt(epsilon(1._TKG))
49reltol
50+0.138777878078144567552953958511352539E-16
51isClose(data, atad(1:size(data)), reltol = reltol)
52T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
53call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
54
55lenData = getUnifRand(5, 100)
56lenData
57+77
58data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
59data
60+1.10037041, +1.73429680, +1.89276564, +1.96428919, +1.20564723, +1.16845989, +1.63098145, +1.60295486, +1.80094695, +1.03141618, +1.44779003, +1.86322546, +1.41387868, +1.25676751, +1.43395627, +1.80150318, +1.94182587, +1.05030549, +1.49288678, +1.23130584, +1.84276998, +1.34783745, +1.25160885, +1.99617648, +1.94534850, +1.86743450, +1.13124454, +1.12340188, +1.70112050, +1.51214957, +1.21358407, +1.10273767, +1.61254048, +1.72690368, +1.18510854, +1.30320954, +1.84651840, +1.17950416, +1.39141560, +1.68665338, +1.36705017, +1.52344537, +1.26580596, +1.64630413, +1.50250006, +1.77579200, +1.16928387, +1.26440001, +1.94807625, +1.12800825, +1.13723135, +1.69862056, +1.54054511, +1.73401690, +1.11066020, +1.65027428, +1.35852671, +1.62755871, +1.93167889, +1.93437982, +1.51673496, +1.35256231, +1.29799652, +1.36147368, +1.61348605, +1.14836359, +1.76909876, +1.35598683, +1.88588428, +1.60186589, +1.08788824, +1.64207888, +1.96505940, +1.65758955, +1.78106356, +1.31404042, +1.14304566
61
62atad = getFFTR(getFFTF(data))
63atad = atad * 2 / size(atad)
64atad
65+1.10037041, +1.73429644, +1.89276528, +1.96428907, +1.20564687, +1.16845965, +1.63098085, +1.60295463, +1.80094719, +1.03141582, +1.44779003, +1.86322570, +1.41387892, +1.25676727, +1.43395627, +1.80150294, +1.94182587, +1.05030537, +1.49288666, +1.23130608, +1.84276986, +1.34783733, +1.25160873, +1.99617624, +1.94534850, +1.86743474, +1.13124478, +1.12340212, +1.70112050, +1.51214957, +1.21358395, +1.10273790, +1.61254072, +1.72690356, +1.18510866, +1.30320954, +1.84651840, +1.17950392, +1.39141560, +1.68665338, +1.36705041, +1.52344537, +1.26580596, +1.64630413, +1.50250006, +1.77579165, +1.16928387, +1.26440001, +1.94807613, +1.12800825, +1.13723111, +1.69862032, +1.54054523, +1.73401654, +1.11066008, +1.65027404, +1.35852647, +1.62755847, +1.93167830, +1.93437982, +1.51673460, +1.35256219, +1.29799640, +1.36147368, +1.61348605, +1.14836347, +1.76909852, +1.35598671, +1.88588440, +1.60186577, +1.08788860, +1.64207888, +1.96505928, +1.65758955, +1.78106368, +1.31404066, +1.14304590, +0.00000000, +0.00000000, +0.238418579E-6, +0.00000000, -0.238418579E-6, +0.119209290E-6, -0.119209290E-6, +0.357627869E-6, +0.00000000, +0.00000000, +0.298023224E-6, +0.596046448E-7, -0.178813934E-6, +0.119209290E-6, -0.119209290E-6, +0.119209290E-6, -0.596046448E-7, -0.178813934E-6, +0.00000000, -0.238418579E-6, -0.238418579E-6, +0.00000000, +0.178813934E-6, +0.00000000, +0.596046448E-7, -0.238418579E-6, +0.536441803E-6, -0.178813934E-6, -0.298023224E-6, -0.178813934E-6, +0.178813934E-6, +0.178813934E-6, -0.596046448E-7, -0.596046448E-7, +0.238418579E-6, +0.119209290E-6, -0.119209290E-6, +0.238418579E-6, +0.357627869E-6, +0.178813934E-6, +0.238418579E-6, -0.178813934E-6, +0.298023224E-6, +0.238418579E-6, +0.00000000, +0.238418579E-6, +0.178813934E-6, +0.298023224E-6, +0.596046448E-7, -0.238418579E-6, +0.119209290E-6
66reltol = sqrt(epsilon(1._TKG))
67reltol
68+0.345266977E-3
69isClose(data, atad(1:size(data)), reltol = reltol)
70T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
71call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
72
73lenData = getUnifRand(5, 100)
74lenData
75+97
76data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
77data
78+1.7720118740884818, +1.0157236229739173, +1.3633776902387282, +1.3023964320343078, +1.3881572665054345, +1.6563177516341816, +1.7381188465800217, +1.8844576874452508, +1.8507551037174017, +1.4383669834760662, +1.2616114259039664, +1.3331313165739875, +1.1733691523022785, +1.4984852098640558, +1.6627703744682996, +1.9965552314823412, +1.8610299205062208, +1.2082161009055810, +1.9799505415482628, +1.4983743715105162, +1.3083485793156688, +1.5061476103665745, +1.2452939754375669, +1.5390868447903996, +1.8184672439970933, +1.8371394994170309, +1.8343132905234776, +1.3616355300483218, +1.4902224105148840, +1.8976719242333426, +1.8146048485072843, +1.0229144186070687, +1.6527286200713052, +1.5814502403430297, +1.7738287514668167, +1.2939214441499516, +1.4318525179946415, +1.2706838591738920, +1.5732757058175013, +1.4714714872356573, +1.3142136313786070, +1.0547968177944234, +1.1987805298953602, +1.4663896733868309, +1.3195158693886273, +1.4433195676696267, +1.4164557149035724, +1.5444599546900819, +1.8669959536281167, +1.2520167144651528, +1.7370724220833369, +1.5523817220076186, +1.0432973581014955, +1.2717604406306169, +1.1096030999933451, +1.6231582674400995, +1.4528153703940916, +1.5663412666236254, +1.1743753086069308, +1.1391984091841512, +1.4892222054352215, +1.3128464778037841, +1.8493299019503269, +1.9737008599724473, +1.4411865278914839, +1.0237195556567311, +1.7517153461689916, +1.4147418966288359, +1.1171362481681137, +1.4472632658416700, +1.0732095962853034, +1.4873638440369739, +1.8923338172720057, +1.0818888348811451, +1.5155945164048099, +1.8111813232499276, +1.3655339118284004, +1.9762651154342252, +1.4220276662215126, +1.9990493062090828, +1.7651926690140027, +1.4295537189111862, +1.0801918438512956, +1.5055302688537087, +1.7774383955302997, +1.0761594897466624, +1.5811411813960001, +1.7416067580132903, +1.1723256767572683, +1.2405403781659901, +1.6972637028085407, +1.9558074713163962, +1.3845130723264285, +1.8177728712828121, +1.7143747643593465, +1.4977961576030212, +1.4802590534661220
79
80atad = getFFTR(getFFTF(data))
81atad = atad * 2 / size(atad)
82atad
83+1.7720118740884816, +1.0157236229739173, +1.3633776902387285, +1.3023964320343080, +1.3881572665054343, +1.6563177516341816, +1.7381188465800212, +1.8844576874452514, +1.8507551037174019, +1.4383669834760660, +1.2616114259039661, +1.3331313165739880, +1.1733691523022785, +1.4984852098640560, +1.6627703744682991, +1.9965552314823412, +1.8610299205062206, +1.2082161009055810, +1.9799505415482623, +1.4983743715105167, +1.3083485793156682, +1.5061476103665745, +1.2452939754375665, +1.5390868447904000, +1.8184672439970933, +1.8371394994170311, +1.8343132905234769, +1.3616355300483225, +1.4902224105148834, +1.8976719242333426, +1.8146048485072834, +1.0229144186070691, +1.6527286200713052, +1.5814502403430297, +1.7738287514668170, +1.2939214441499516, +1.4318525179946417, +1.2706838591738920, +1.5732757058175011, +1.4714714872356571, +1.3142136313786072, +1.0547968177944229, +1.1987805298953602, +1.4663896733868316, +1.3195158693886273, +1.4433195676696269, +1.4164557149035726, +1.5444599546900819, +1.8669959536281169, +1.2520167144651531, +1.7370724220833367, +1.5523817220076186, +1.0432973581014962, +1.2717604406306173, +1.1096030999933451, +1.6231582674400993, +1.4528153703940925, +1.5663412666236254, +1.1743753086069306, +1.1391984091841512, +1.4892222054352215, +1.3128464778037836, +1.8493299019503269, +1.9737008599724466, +1.4411865278914835, +1.0237195556567311, +1.7517153461689914, +1.4147418966288356, +1.1171362481681140, +1.4472632658416700, +1.0732095962853032, +1.4873638440369736, +1.8923338172720057, +1.0818888348811446, +1.5155945164048092, +1.8111813232499279, +1.3655339118284004, +1.9762651154342250, +1.4220276662215121, +1.9990493062090828, +1.7651926690140025, +1.4295537189111860, +1.0801918438512956, +1.5055302688537084, +1.7774383955302995, +1.0761594897466624, +1.5811411813960001, +1.7416067580132903, +1.1723256767572683, +1.2405403781659896, +1.6972637028085400, +1.9558074713163964, +1.3845130723264287, +1.8177728712828114, +1.7143747643593470, +1.4977961576030205, +1.4802590534661215, -0.11102230246251565E-15, +0.22204460492503131E-15, -0.33306690738754696E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.88817841970012523E-15, +0.66613381477509392E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.44408920985006262E-15, +0.55511151231257827E-15, +0.22204460492503131E-15, +0.77715611723760958E-15, +0.66613381477509392E-15, +0.66613381477509392E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.66613381477509392E-15, +0.66613381477509392E-15, +0.11102230246251565E-15, +0.77715611723760958E-15, +0.44408920985006262E-15, +0.11102230246251565E-14
84reltol = sqrt(epsilon(1._TKG))
85reltol
86+0.14901161193847656E-7
87isClose(data, atad(1:size(data)), reltol = reltol)
88T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
89call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
90
91lenData = getUnifRand(5, 100)
92lenData
93+94
94data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
95data
96+1.62492801755635472713878453440028192, +1.18497411457695004512500551144138741, +1.86558818294644980735060374964292288, +1.93717952087641164488042017393604459, +1.89402979316823828773880016208323214, +1.01816613831268696760743523170855221, +1.07366219187542392724406317996148793, +1.22205766269214731808880568665957545, +1.60463048043548833445044711295231476, +1.76470619538743426213141708436782537, +1.85418117387823531807572876624055729, +1.96118337527858026794570493293623167, +1.86314881557852085706100910773647132, +1.81073611820269295393852786328073375, +1.98030516725939696033672450068778622, +1.42457473804255340560376857885861215, +1.90526817624918407413620677077307611, +1.56592346572596880497805276873040378, +1.98103924467920605751967400429480987, +1.57784675750398842432620585918523825, +1.13285213485598631141044249204330659, +1.53719344090473534480522585460081302, +1.96107120665295299574090565876559353, +1.86596509742989354365163487817323297, +1.60818606282930517170055075201510419, +1.01125289391123605121692194849631982, +1.17168836648776935021313731571161571, +1.27218262403899328211038952631539083, +1.10972203738980707208303926225659714, +1.53044254538593261754810159938277093, +1.15716020045771856853419241678575387, +1.81177051644007236349607318218933341, +1.79116368488550839766293555616589930, +1.95139644741514755908644677491529972, +1.22803791999487527307705037111951711, +1.59920464591577950678831889609568816, +1.17853141564656540796101400391262941, +1.61457842017123654580582891086216789, +1.46691871865433860156954868300960245, +1.90537394066656463649865026652602056, +1.98198212208007832368966662767074395, +1.49897885211123225950831515653896642, +1.75278896401824586464792789305631884, +1.23492950775078884983055019505804324, +1.96732065970980141961132740921040012, +1.20807128785616787432292571046945532, +1.68269860182381818042499738949669394, +1.25677666350600578737065200216485099, +1.29357978559856823772716582122839413, +1.38444311441583890361024764909032840, +1.27589858381450244546284254445498039, +1.35018799342243091501589594761360350, +1.87036300054827044052481497786125854, +1.65798349246911768015118468735865807, +1.27424957551327609498837972339972972, +1.14284040847527508475612803874613202, +1.76541123683741268045375974382394447, +1.20652838541029068396876592776845673, +1.48087993841001473332494769613635523, +1.50179508705651413429214645466071917, +1.48273825460701168070834453710404185, +1.37506681588651161915843352067257855, +1.59608912857959013058230007505095249, +1.96666838502918661214280614294511878, +1.99021547299954323798042425863772953, +1.79679663303590649336902090574287048, +1.51508141136187846537725288082591039, +1.49015537461568253946812905175007244, +1.06994216610121841981830703078740708, +1.00594413985801334590520082749653814, +1.27014206882701639969051368678520979, +1.73387540402852238671701990542955731, +1.37330873545846376238207493726025984, +1.18820698540090827285225406176837590, +1.84886564852884662442153663400222241, +1.80359775676185401926728726798213418, +1.89963039005856071560688933130321864, +1.58265433703655203954571151269493140, +1.70016579233456728734697087538715880, +1.08664140926783459823762357410902748, +1.13171230148992993093487716569466634, +1.77855625825024071367237739031425704, +1.20763799129642342738644643501707770, +1.50979278638921260473103956830913937, +1.57229623894620854523174563466380916, +1.94786984247952010160817370239423191, +1.60150357504501989552767561210473626, +1.49717920430711394153355316441025818, +1.07676904387582843674058686725949605, +1.90464405418125750193123346885053086, +1.75726923147212490981965351700811775, +1.94947299617461774040589736276773549, +1.57993225752577196587252906538750811, +1.28028871365499016583619717824085052
97
98atad = getFFTR(getFFTF(data))
99atad = atad * 2 / size(atad)
100atad
101+1.62492801755635472713878453440028212, +1.18497411457695004512500551144138760, +1.86558818294644980735060374964292327, +1.93717952087641164488042017393604517, +1.89402979316823828773880016208323194, +1.01816613831268696760743523170855240, +1.07366219187542392724406317996148774, +1.22205766269214731808880568665957603, +1.60463048043548833445044711295231515, +1.76470619538743426213141708436782537, +1.85418117387823531807572876624055806, +1.96118337527858026794570493293623263, +1.86314881557852085706100910773647170, +1.81073611820269295393852786328073394, +1.98030516725939696033672450068778699, +1.42457473804255340560376857885861215, +1.90526817624918407413620677077307611, +1.56592346572596880497805276873040397, +1.98103924467920605751967400429480967, +1.57784675750398842432620585918523883, +1.13285213485598631141044249204330678, +1.53719344090473534480522585460081340, +1.96107120665295299574090565876559372, +1.86596509742989354365163487817323336, +1.60818606282930517170055075201510438, +1.01125289391123605121692194849632021, +1.17168836648776935021313731571161610, +1.27218262403899328211038952631539083, +1.10972203738980707208303926225659695, +1.53044254538593261754810159938277112, +1.15716020045771856853419241678575349, +1.81177051644007236349607318218933379, +1.79116368488550839766293555616589930, +1.95139644741514755908644677491529953, +1.22803791999487527307705037111951749, +1.59920464591577950678831889609568797, +1.17853141564656540796101400391262922, +1.61457842017123654580582891086216769, +1.46691871865433860156954868300960265, +1.90537394066656463649865026652602075, +1.98198212208007832368966662767074433, +1.49897885211123225950831515653896642, +1.75278896401824586464792789305631922, +1.23492950775078884983055019505804305, +1.96732065970980141961132740921040031, +1.20807128785616787432292571046945512, +1.68269860182381818042499738949669413, +1.25677666350600578737065200216485099, +1.29357978559856823772716582122839394, +1.38444311441583890361024764909032840, +1.27589858381450244546284254445498020, +1.35018799342243091501589594761360389, +1.87036300054827044052481497786125892, +1.65798349246911768015118468735865807, +1.27424957551327609498837972339972991, +1.14284040847527508475612803874613241, +1.76541123683741268045375974382394427, +1.20652838541029068396876592776845693, +1.48087993841001473332494769613635523, +1.50179508705651413429214645466071917, +1.48273825460701168070834453710404224, +1.37506681588651161915843352067257836, +1.59608912857959013058230007505095230, +1.96666838502918661214280614294511916, +1.99021547299954323798042425863772953, +1.79679663303590649336902090574287029, +1.51508141136187846537725288082591039, +1.49015537461568253946812905175007283, +1.06994216610121841981830703078740727, +1.00594413985801334590520082749653795, +1.27014206882701639969051368678521017, +1.73387540402852238671701990542955789, +1.37330873545846376238207493726026023, +1.18820698540090827285225406176837629, +1.84886564852884662442153663400222279, +1.80359775676185401926728726798213495, +1.89963039005856071560688933130321883, +1.58265433703655203954571151269493159, +1.70016579233456728734697087538715899, +1.08664140926783459823762357410902787, +1.13171230148992993093487716569466634, +1.77855625825024071367237739031425704, +1.20763799129642342738644643501707770, +1.50979278638921260473103956830913956, +1.57229623894620854523174563466380916, +1.94786984247952010160817370239423191, +1.60150357504501989552767561210473665, +1.49717920430711394153355316441025818, +1.07676904387582843674058686725949547, +1.90464405418125750193123346885053124, +1.75726923147212490981965351700811736, +1.94947299617461774040589736276773588, +1.57993225752577196587252906538750811, +1.28028871365499016583619717824085052, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33, -0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33, -0.481482486096808963263994485646231830E-33, +0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, +0.192592994438723585305597794258492732E-33, -0.577778983316170755916793382775478196E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33, +0.481482486096808963263994485646231830E-33
102reltol = sqrt(epsilon(1._TKG))
103reltol
104+0.138777878078144567552953958511352539E-16
105isClose(data, atad(1:size(data)), reltol = reltol)
106T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
107call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
108
109lenData = getUnifRand(5, 100)
110lenData
111+7
112data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
113data
114(+1.45257950, +0.400623083), (+1.79976058, +0.238606513), (+1.33070362, +0.133118153), (+1.85974383, +0.483960330), (+1.66437030, +0.338210464), (+1.91242743, +0.725806594), (+1.17974782, +0.680050731)
115
116atad = getFFTR(getFFTF(data))
117atad = atad / size(atad)
118atad
119(+1.45257962, +0.400623083), (+1.79976058, +0.238606632), (+1.33070350, +0.133118182), (+1.85974360, +0.483960152), (+1.66437042, +0.338210464), (+1.91242719, +0.725806475), (+1.17974782, +0.680050731), (+0.298023224E-6, +0.596046448E-7)
120reltol = sqrt(epsilon(1._TKG))
121reltol
122+0.345266977E-3
123isClose(data, atad(1:size(data)), reltol = reltol)
124T, T, T, T, T, T, T
125call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
126
127lenData = getUnifRand(5, 100)
128lenData
129+83
130data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
131data
132(+1.5649536261375654, +0.33636755025934617), (+1.2340254812683040, +0.65371914736655212), (+1.7370725682493080, +0.54485127586614834E-1), (+1.2980195136664432, +0.43520240412546818), (+1.4068186844924200, +0.18655328061115117), (+1.7746368630676630, +0.48921946432267649), (+1.2418619625429388, +0.86526108150440473), (+1.2932868425375319, +0.16734014378917494), (+1.1563106092925832, +0.57196342376707121), (+1.5425941687492339, +0.79570229104589663E-2), (+1.8081373178683444, +0.78439164194059785), (+1.1338776679826854, +0.26737408107555272), (+1.9536705729627721, +0.60353278280057021), (+1.3770057678533845, +0.95087956997773959), (+1.4704038860782016, +0.94757569030708244), (+1.0464826092650377, +0.65604647713421615), (+1.1637218740913711, +0.31153698611168890), (+1.9649207496029151, +0.81566280465114072), (+1.5083983339939009, +0.47147407236723582), (+1.2623369869845020, +0.96988138340964036), (+1.8784017544912046, +0.52066775900048445), (+1.3793604261362571, +0.48272946216285684), (+1.3728639900597819, +0.98350149910641216), (+1.4465464029978405, +0.63715253342723488), (+1.1439530981314505, +0.88016813799282967), (+1.0068068932378069, +0.16327501248721465), (+1.0545813669904143, +0.22676370730556650), (+1.5703666496610971, +0.82890667045438848), (+1.5093046384500624, +0.57236118592909035), (+1.3722851368930558, +0.17012011693931262), (+1.5039676112072757, +0.99471141225302084), (+1.8541235117195627, +0.18680007543711041), (+1.9414830963300012, +0.10492781844177468), (+1.4754617513416910, +0.24406290687010612E-1), (+1.0428376619025377, +0.25413855193289137), (+1.7898005141104039, +0.80146011628643177), (+1.9573568228490967, +0.69861360367714020), (+1.8640763180341700, +0.82273527979191907), (+1.7630679405298073, +0.44204663184607329), (+1.7545636709369692, +0.48397724253632035), (+1.8308720759879429, +0.27651351018300785), (+1.2359525428933273, +0.59282855161296943), (+1.1973790805629068, +0.33512474852333374), (+1.7152673192002030, +0.15651093303385344), (+1.4096322921468061, +0.45456878864232675), (+1.0771607400295982, +0.57128228151190164), (+1.7804555725074582, +0.54286049450444118), (+1.0302170805821764, +0.13718094512681023E-1), (+1.2800453635035103, +0.42553398493775774), (+1.8528552670421026, +0.31879447733037913), (+1.2731626547992283, +0.78012167594318149), (+1.0285850481665415, +0.42957120706507845), (+1.4537150260202829, +0.71701544672712947), (+1.3955424245918637, +0.92954955957814001), (+1.8253636345297850, +0.49241448009813904), (+1.4397997601756853, +0.76124582504506544), (+1.7510943710173492, +0.31502258637292802), (+1.4030878383615695, +0.77456887386903039E-1), (+1.3171361093185276, +0.53142026753471172), (+1.4992198715616940, +0.58610343811437793), (+1.2497119675053994, +0.62690725411767945), (+1.1696895988214862, +0.63326809605132328), (+1.3722271818371321, +0.80990406861842068), (+1.7870197788210653, +0.85535933628636773), (+1.7160717905586067, +0.20197217599403594), (+1.5927115283522095, +0.40746056476737280), (+1.4944486329044482, +0.99458262780081386), (+1.4023671178216390, +0.78402025209850001), (+1.3948503415124365, +0.51860587514435486), (+1.9557336303309238, +0.17776874648273522), (+1.7496427552440359, +0.66049670383104708), (+1.8957612824471106, +0.62743365681251939E-1), (+1.9793772005949637, +0.10062396474484359), (+1.3374629295882654, +0.23236115329828533), (+1.1444766926504539, +0.49231542595326194), (+1.2340861684455493, +0.91402245358347722), (+1.9080983198487980, +0.35275405633059398), (+1.9807234441952244, +0.59055027886972811), (+1.2213127796428132, +0.22323401152076894), (+1.6048287358956492, +0.59900441476987820), (+1.6798515103181062, +0.81044526069180745), (+1.2179426896339129, +0.27478821965689626), (+1.1344833508299046, +0.66425108589823312)
133
134atad = getFFTR(getFFTF(data))
135atad = atad / size(atad)
136atad
137(+1.5649536261375661, +0.33636755025934623), (+1.2340254812683045, +0.65371914736655234), (+1.7370725682493084, +0.54485127586614890E-1), (+1.2980195136664436, +0.43520240412546851), (+1.4068186844924198, +0.18655328061115134), (+1.7746368630676630, +0.48921946432267682), (+1.2418619625429388, +0.86526108150440495), (+1.2932868425375321, +0.16734014378917503), (+1.1563106092925834, +0.57196342376707143), (+1.5425941687492342, +0.79570229104592993E-2), (+1.8081373178683446, +0.78439164194059829), (+1.1338776679826854, +0.26737408107555283), (+1.9536705729627719, +0.60353278280057054), (+1.3770057678533840, +0.95087956997774015), (+1.4704038860782014, +0.94757569030708244), (+1.0464826092650372, +0.65604647713421649), (+1.1637218740913711, +0.31153698611168901), (+1.9649207496029151, +0.81566280465114083), (+1.5083983339939011, +0.47147407236723604), (+1.2623369869845020, +0.96988138340964036), (+1.8784017544912039, +0.52066775900048445), (+1.3793604261362571, +0.48272946216285684), (+1.3728639900597819, +0.98350149910641216), (+1.4465464029978401, +0.63715253342723488), (+1.1439530981314507, +0.88016813799282967), (+1.0068068932378065, +0.16327501248721474), (+1.0545813669904145, +0.22676370730556655), (+1.5703666496610973, +0.82890667045438826), (+1.5093046384500619, +0.57236118592909013), (+1.3722851368930555, +0.17012011693931267), (+1.5039676112072753, +0.99471141225302073), (+1.8541235117195620, +0.18680007543711052), (+1.9414830963300016, +0.10492781844177443), (+1.4754617513416908, +0.24406290687010314E-1), (+1.0428376619025381, +0.25413855193289114), (+1.7898005141104041, +0.80146011628643166), (+1.9573568228490967, +0.69861360367713976), (+1.8640763180341700, +0.82273527979191885), (+1.7630679405298071, +0.44204663184607296), (+1.7545636709369690, +0.48397724253632013), (+1.8308720759879431, +0.27651351018300763), (+1.2359525428933273, +0.59282855161296943), (+1.1973790805629068, +0.33512474852333374), (+1.7152673192002033, +0.15651093303385322), (+1.4096322921468059, +0.45456878864232642), (+1.0771607400295977, +0.57128228151190141), (+1.7804555725074580, +0.54286049450444118), (+1.0302170805821760, +0.13718094512680690E-1), (+1.2800453635035105, +0.42553398493775763), (+1.8528552670421023, +0.31879447733037897), (+1.2731626547992283, +0.78012167594318105), (+1.0285850481665415, +0.42957120706507823), (+1.4537150260202829, +0.71701544672712902), (+1.3955424245918637, +0.92954955957813956), (+1.8253636345297850, +0.49241448009813860), (+1.4397997601756851, +0.76124582504506511), (+1.7510943710173494, +0.31502258637292774), (+1.4030878383615693, +0.77456887386902817E-1), (+1.3171361093185281, +0.53142026753471150), (+1.4992198715616942, +0.58610343811437771), (+1.2497119675053998, +0.62690725411767900), (+1.1696895988214862, +0.63326809605132306), (+1.3722271818371323, +0.80990406861842013), (+1.7870197788210649, +0.85535933628636718), (+1.7160717905586071, +0.20197217599403577), (+1.5927115283522097, +0.40746056476737269), (+1.4944486329044486, +0.99458262780081363), (+1.4023671178216390, +0.78402025209849979), (+1.3948503415124367, +0.51860587514435474), (+1.9557336303309236, +0.17776874648273513), (+1.7496427552440359, +0.66049670383104686), (+1.8957612824471106, +0.62743365681251856E-1), (+1.9793772005949637, +0.10062396474484353), (+1.3374629295882652, +0.23236115329828549), (+1.1444766926504542, +0.49231542595326205), (+1.2340861684455489, +0.91402245358347745), (+1.9080983198487982, +0.35275405633059365), (+1.9807234441952239, +0.59055027886972811), (+1.2213127796428134, +0.22323401152076872), (+1.6048287358956488, +0.59900441476987765), (+1.6798515103181062, +0.81044526069180733), (+1.2179426896339129, +0.27478821965689615), (+1.1344833508299050, +0.66425108589823301), (-0.11102230246251565E-15, -0.55511151231257827E-15), (+0.77715611723760958E-15, -0.16653345369377348E-15), (+0.55511151231257827E-15, -0.19428902930940239E-15), (+0.55511151231257827E-15, -0.55511151231257827E-16), (+0.11102230246251565E-15, -0.11102230246251565E-15), (+0.33306690738754696E-15, -0.16653345369377348E-15), (-0.11102230246251565E-15, -0.13877787807814457E-15), (+0.22204460492503131E-15, -0.12490009027033011E-15), (+0.33306690738754696E-15, -0.11102230246251565E-15), (+0.55511151231257827E-15, -0.11102230246251565E-15), (+0.44408920985006262E-15, -0.26367796834847468E-15), (+0.99920072216264089E-15, +0.0000000000000000), (+0.44408920985006262E-15, -0.55511151231257827E-16), (+0.33306690738754696E-15, +0.25673907444456745E-15), (+0.0000000000000000, -0.14571677198205180E-15), (+0.11102230246251565E-15, +0.83266726846886741E-16), (+0.0000000000000000, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.27755575615628914E-15), (+0.33306690738754696E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.36082248300317588E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.33306690738754696E-15), (+0.0000000000000000, +0.0000000000000000), (-0.11102230246251565E-15, +0.0000000000000000), (+0.22204460492503131E-15, +0.11102230246251565E-15), (+0.66613381477509392E-15, +0.33306690738754696E-15), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.44408920985006262E-15, +0.44408920985006262E-15), (+0.22204460492503131E-15, +0.19428902930940239E-15), (+0.22204460492503131E-15, +0.55511151231257827E-16), (+0.11102230246251565E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.83266726846886741E-16), (+0.0000000000000000, +0.49960036108132044E-15), (+0.33306690738754696E-15, +0.44408920985006262E-15), (+0.44408920985006262E-15, +0.69388939039072284E-15), (+0.22204460492503131E-15, +0.49960036108132044E-15), (+0.33306690738754696E-15, +0.22204460492503131E-15), (+0.33306690738754696E-15, +0.62450045135165055E-16), (+0.11102230246251565E-15, +0.44408920985006262E-15), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.33306690738754696E-15, +0.44408920985006262E-15), (+0.22204460492503131E-15, +0.55511151231257827E-15), (+0.0000000000000000, +0.55511151231257827E-15), (+0.33306690738754696E-15, +0.88817841970012523E-15)
138reltol = sqrt(epsilon(1._TKG))
139reltol
140+0.14901161193847656E-7
141isClose(data, atad(1:size(data)), reltol = reltol)
142T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
143call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
144
145lenData = getUnifRand(5, 100)
146lenData
147+10
148data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
149data
150(+1.33693313234722755336820922914836339, +0.144613931201916107358556709645708737), (+1.44129880914865046533539550644261862, +0.612988416151765332130506104149110578), (+1.57245970269833024669387800811416871, +0.797080166150621195307615611334330887), (+1.49868349416069847127064166875506174, +0.588610709980024807063872253240282833), (+1.79329935867143156423952371276544280, +0.994198403644318320044548325615889734), (+1.92832064697307943021759084399440073, +0.986451228231987500624565078793799359), (+1.67828122837767814458726544623171426, +0.631345217554096185087301855986068398), (+1.25945268188046208634004542337780408, +0.389259175087823253992395592511296695), (+1.89680529180240995444483938497975378, +0.256016966333653388053832863139362709), (+1.51770290141534337042997633936956952, +0.741630833732605419913615588497187768)
151
152atad = getFFTR(getFFTF(data))
153atad = atad / size(atad)
154atad
155(+1.33693313234722755336820922914836358, +0.144613931201916107358556709645708641), (+1.44129880914865046533539550644261881, +0.612988416151765332130506104149110578), (+1.57245970269833024669387800811416871, +0.797080166150621195307615611334330887), (+1.49868349416069847127064166875506193, +0.588610709980024807063872253240283025), (+1.79329935867143156423952371276544318, +0.994198403644318320044548325615889734), (+1.92832064697307943021759084399440112, +0.986451228231987500624565078793799359), (+1.67828122837767814458726544623171465, +0.631345217554096185087301855986068205), (+1.25945268188046208634004542337780427, +0.389259175087823253992395592511296599), (+1.89680529180240995444483938497975398, +0.256016966333653388053832863139362709), (+1.51770290141534337042997633936956933, +0.741630833732605419913615588497187768), (+0.962964972193617926527988971292463659E-34, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, -0.240741243048404481631997242823115915E-33), (-0.288889491658085377958396691387739098E-33, +0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, -0.120370621524202240815998621411557957E-33)
156reltol = sqrt(epsilon(1._TKG))
157reltol
158+0.138777878078144567552953958511352539E-16
159isClose(data, atad(1:size(data)), reltol = reltol)
160T, T, T, T, T, T, T, T, T, T
161call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
162
163lenData = getUnifRand(5, 100)
164lenData
165+17
166data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
167data
168+1.92495608, +1.08376551, +1.51416206, +1.26475251, +1.91540027, +1.28899229, +1.39950335, +1.56070089, +1.11039495, +1.48767757, +1.72371936, +1.40717411, +1.72107124, +1.81615651, +1.07019150, +1.98237503, +1.55418563
169
170atad = getFFTR(getFFTF(data))
171atad = atad * 2 / size(atad)
172atad
173+1.92495608, +1.08376551, +1.51416183, +1.26475263, +1.91540003, +1.28899217, +1.39950299, +1.56070089, +1.11039507, +1.48767757, +1.72371936, +1.40717399, +1.72107136, +1.81615591, +1.07019138, +1.98237467, +1.55418563, +0.596046448E-7, +0.596046448E-7, -0.178813934E-6, +0.357627869E-6, +0.178813934E-6, +0.238418579E-6, +0.00000000, -0.119209290E-6, +0.596046448E-7, -0.596046448E-7, -0.119209290E-6, +0.00000000, +0.536441803E-6, -0.596046448E-7, +0.238418579E-6
174reltol = sqrt(epsilon(1._TKG))
175reltol
176+0.345266977E-3
177isClose(data, atad(1:size(data)), reltol = reltol)
178T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
179call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
180
181lenData = getUnifRand(5, 100)
182lenData
183+77
184data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
185data
186+1.7484100157783757, +1.0063270519331642, +1.3935096953222541, +1.9211831041238669, +1.2573156659305083, +1.7181534930103646, +1.5957178995997447, +1.1607167833361669, +1.3430202273420093, +1.1871223995507656, +1.0573532237465810, +1.4871584818648174, +1.2773712825058441, +1.1486698456451698, +1.9274040478127779, +1.2747268778121263, +1.9868291103894009, +1.5423160184764071, +1.6439784764661454, +1.5077948757613395, +1.5725002405929103, +1.8215790255598994, +1.1488095110214902, +1.1806299078648923, +1.2780580864267723, +1.2677009136722643, +1.3573831449375060, +1.8155297350219437, +1.7838750294149404, +1.7039545845619184, +1.8044993958462201, +1.3236735192076732, +1.9684448824987277, +1.3766193545953942, +1.0489768299784554, +1.0758241289076396, +1.9369174887230196, +1.5626304171552070, +1.1392790951709930, +1.5424405252597442, +1.3821379684081090, +1.0888130970649188, +1.6009818345377673, +1.1120067075163687, +1.9784333627509638, +1.5351119707321219, +1.9268443116959584, +1.8636567738041185, +1.1547666636280423, +1.9379448875096759, +1.0985336444761524, +1.2383172749022280, +1.7094189107821405, +1.0183488819471376, +1.9187674606896856, +1.1270252684327093, +1.1596755590076429, +1.3230360354929966, +1.7849086994015688, +1.8997561675473091, +1.7498818782399654, +1.2342956026431353, +1.5540375803903679, +1.4258828779524921, +1.2432663025393249, +1.2201007649810052, +1.1322992272583547, +1.6941366933465529, +1.4419638014834559, +1.3414897375452157, +1.7708958944882636, +1.7450092909969093, +1.1036208957156979, +1.9356121959287442, +1.4384001485718296, +1.9492574063855850, +1.0851655465738748
187
188atad = getFFTR(getFFTF(data))
189atad = atad * 2 / size(atad)
190atad
191+1.7484100157783757, +1.0063270519331642, +1.3935096953222543, +1.9211831041238672, +1.2573156659305080, +1.7181534930103644, +1.5957178995997447, +1.1607167833361671, +1.3430202273420093, +1.1871223995507654, +1.0573532237465812, +1.4871584818648178, +1.2773712825058443, +1.1486698456451698, +1.9274040478127783, +1.2747268778121263, +1.9868291103894009, +1.5423160184764071, +1.6439784764661454, +1.5077948757613397, +1.5725002405929100, +1.8215790255598989, +1.1488095110214902, +1.1806299078648923, +1.2780580864267719, +1.2677009136722646, +1.3573831449375056, +1.8155297350219439, +1.7838750294149399, +1.7039545845619180, +1.8044993958462197, +1.3236735192076736, +1.9684448824987277, +1.3766193545953938, +1.0489768299784559, +1.0758241289076393, +1.9369174887230198, +1.5626304171552063, +1.1392790951709937, +1.5424405252597440, +1.3821379684081092, +1.0888130970649188, +1.6009818345377682, +1.1120067075163689, +1.9784333627509643, +1.5351119707321212, +1.9268443116959588, +1.8636567738041183, +1.1547666636280423, +1.9379448875096754, +1.0985336444761526, +1.2383172749022275, +1.7094189107821407, +1.0183488819471371, +1.9187674606896856, +1.1270252684327091, +1.1596755590076424, +1.3230360354929964, +1.7849086994015693, +1.8997561675473089, +1.7498818782399654, +1.2342956026431346, +1.5540375803903674, +1.4258828779524917, +1.2432663025393249, +1.2201007649810052, +1.1322992272583545, +1.6941366933465531, +1.4419638014834562, +1.3414897375452155, +1.7708958944882640, +1.7450092909969090, +1.1036208957156974, +1.9356121959287442, +1.4384001485718292, +1.9492574063855854, +1.0851655465738752, +0.11102230246251565E-15, +0.11102230246251565E-15, -0.55511151231257827E-15, +0.33306690738754696E-15, -0.33306690738754696E-15, +0.0000000000000000, -0.44408920985006262E-15, +0.22204460492503131E-15, -0.11102230246251565E-15, +0.66613381477509392E-15, +0.0000000000000000, +0.0000000000000000, -0.11102230246251565E-15, +0.77715611723760958E-15, +0.33306690738754696E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, +0.11102230246251565E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, +0.77715611723760958E-15, +0.22204460492503131E-15, +0.22204460492503131E-15, -0.22204460492503131E-15, -0.11102230246251565E-15, -0.11102230246251565E-15, +0.22204460492503131E-15, -0.33306690738754696E-15, +0.66613381477509392E-15, -0.55511151231257827E-15, +0.33306690738754696E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, -0.33306690738754696E-15, +0.99920072216264089E-15, +0.22204460492503131E-15, +0.88817841970012523E-15, +0.11102230246251565E-15, +0.44408920985006262E-15, +0.0000000000000000, +0.77715611723760958E-15, -0.22204460492503131E-15, +0.11102230246251565E-14, +0.22204460492503131E-15, +0.99920072216264089E-15
192reltol = sqrt(epsilon(1._TKG))
193reltol
194+0.14901161193847656E-7
195isClose(data, atad(1:size(data)), reltol = reltol)
196T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
197call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
198
199lenData = getUnifRand(5, 100)
200lenData
201+14
202data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
203data
204+1.93943279371084191564350219050119886, +1.06026660546543866769885752657342070, +1.79131557361156736716408172174613074, +1.10575472967593195583772273429367577, +1.83087431077871999770363925899213426, +1.96169634980997533338658009873063654, +1.99354631664316207287352375859562718, +1.39807601636086839574071386904762045, +1.35169589563126668506959265322753813, +1.28779555485128892528064712708368006, +1.81019851665997160449121093262296017, +1.52918628256705026955364025018485669, +1.05456642650301057312893064590814276, +1.65010914411414959533865401455535982
205
206atad = getFFTR(getFFTF(data))
207atad = atad * 2 / size(atad)
208atad
209+1.93943279371084191564350219050119925, +1.06026660546543866769885752657342090, +1.79131557361156736716408172174613113, +1.10575472967593195583772273429367596, +1.83087431077871999770363925899213445, +1.96169634980997533338658009873063654, +1.99354631664316207287352375859562718, +1.39807601636086839574071386904762045, +1.35169589563126668506959265322753851, +1.28779555485128892528064712708368006, +1.81019851665997160449121093262296036, +1.52918628256705026955364025018485669, +1.05456642650301057312893064590814295, +1.65010914411414959533865401455536002, +0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000
210reltol = sqrt(epsilon(1._TKG))
211reltol
212+0.138777878078144567552953958511352539E-16
213isClose(data, atad(1:size(data)), reltol = reltol)
214T, T, T, T, T, T, T, T, T, T, T, T, T, T
215call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
216
217lenData = getUnifRand(5, 100)
218lenData
219+66
220data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
221data
222(+1.08404005, +0.568813860), (+1.38032246, +0.664228678), (+1.36022615, +0.355806112), (+1.01634502, +0.473186672), (+1.07729626, +0.164022207), (+1.19799662, +0.304795444), (+1.45292139, +0.452005506), (+1.76020646, +0.188592613), (+1.14376450, +0.970788360), (+1.62565124, +0.459893167), (+1.01604342, +0.576315045), (+1.23303056, +0.362817049), (+1.53047991, +0.911913455), (+1.68206382, +0.924907148), (+1.30215645, +0.444475949), (+1.44748366, +0.272559166), (+1.33549690, +0.353024542), (+1.40837765, +0.404938459), (+1.24766874, +0.684930086), (+1.56318188, +0.694771230), (+1.67323160, +0.937480986), (+1.63477898, +0.866047025), (+1.46535778, +0.130739748), (+1.18089223, +0.305128396), (+1.12794995, +0.752933681), (+1.33616877, +0.755569458), (+1.09175730, +0.368503928E-1), (+1.92594826, +0.594405293), (+1.00069404, +0.235885382), (+1.72138453, +0.281744421), (+1.04165316, +0.448950350), (+1.58339047, +0.148095191), (+1.90593255, +0.600207031), (+1.75400746, +0.248197198), (+1.58714736, +0.388743937), (+1.53050375, +0.604283154), (+1.94136119, +0.884517729), (+1.51390123, +0.176856399), (+1.59458363, +0.185382783), (+1.26774955, +0.728048325), (+1.24946678, +0.912906349), (+1.27749133, +0.577240288), (+1.50748253, +0.861298442), (+1.06787598, +0.760634184), (+1.97333837, +0.877330005), (+1.03687596, +0.108411849), (+1.34216523, +0.396409631), (+1.76133990, +0.436214089), (+1.18734145, +0.197110891), (+1.59632552, +0.771805227), (+1.04874277, +0.503668725), (+1.06284070, +0.561681986E-1), (+1.00147414, +0.988090217), (+1.20531571, +0.702332258E-1), (+1.51837230, +0.585083783), (+1.40695941, +0.579930544), (+1.43278646, +0.391511023), (+1.85523343, +0.602372825), (+1.54049563, +0.198615193), (+1.39333630, +0.354721487), (+1.99234390, +0.197407782), (+1.66968918, +0.721269548), (+1.09742713, +0.413782656), (+1.91829813, +0.890558839), (+1.89922929, +0.620601356), (+1.22010469, +0.651406884)
223
224atad = getFFTR(getFFTF(data))
225atad = atad / size(atad)
226atad
227(+1.08403993, +0.568813920), (+1.38032246, +0.664228797), (+1.36022592, +0.355806172), (+1.01634479, +0.473186612), (+1.07729602, +0.164022207), (+1.19799662, +0.304795444), (+1.45292091, +0.452005327), (+1.76020598, +0.188592523), (+1.14376450, +0.970788360), (+1.62565136, +0.459893405), (+1.01604342, +0.576315045), (+1.23303080, +0.362817079), (+1.53047979, +0.911913395), (+1.68206382, +0.924907446), (+1.30215633, +0.444475949), (+1.44748366, +0.272559047), (+1.33549690, +0.353024542), (+1.40837753, +0.404938579), (+1.24766850, +0.684930027), (+1.56318164, +0.694771111), (+1.67323136, +0.937480986), (+1.63477874, +0.866047025), (+1.46535754, +0.130739719), (+1.18089199, +0.305128455), (+1.12794995, +0.752933741), (+1.33616877, +0.755569756), (+1.09175718, +0.368504785E-1), (+1.92594814, +0.594405532), (+1.00069404, +0.235885352), (+1.72138453, +0.281744719), (+1.04165304, +0.448950380), (+1.58339047, +0.148095310), (+1.90593255, +0.600206912), (+1.75400734, +0.248197168), (+1.58714712, +0.388743669), (+1.53050375, +0.604282975), (+1.94136119, +0.884517312), (+1.51390123, +0.176856294), (+1.59458327, +0.185382485), (+1.26774955, +0.728048086), (+1.24946678, +0.912906289), (+1.27749121, +0.577240348), (+1.50748229, +0.861298203), (+1.06787586, +0.760634184), (+1.97333837, +0.877329946), (+1.03687608, +0.108411789), (+1.34216511, +0.396409512), (+1.76133990, +0.436214030), (+1.18734121, +0.197110742), (+1.59632528, +0.771805108), (+1.04874265, +0.503668547), (+1.06284058, +0.561681688E-1), (+1.00147426, +0.988090038), (+1.20531583, +0.702329874E-1), (+1.51837206, +0.585083604), (+1.40695930, +0.579930186), (+1.43278635, +0.391511083), (+1.85523307, +0.602372944), (+1.54049551, +0.198615015), (+1.39333606, +0.354721427), (+1.99234366, +0.197407871), (+1.66968918, +0.721269369), (+1.09742713, +0.413782597), (+1.91829789, +0.890558600), (+1.89922929, +0.620601296), (+1.22010469, +0.651406884), (+0.178813934E-6, +0.00000000), (+0.178813934E-6, +0.447034836E-7), (+0.178813934E-6, +0.670552254E-7), (+0.00000000, -0.447034836E-7), (-0.596046448E-7, +0.134110451E-6), (+0.238418579E-6, +0.149011612E-6), (-0.596046448E-7, +0.00000000), (-0.178813934E-6, -0.596046448E-7), (+0.00000000, +0.00000000), (-0.596046448E-7, -0.894069672E-7), (-0.119209290E-6, +0.00000000), (+0.00000000, -0.268220901E-6), (-0.119209290E-6, +0.447034836E-7), (-0.119209290E-6, +0.149011612E-7), (-0.596046448E-7, -0.149011612E-7), (+0.119209290E-6, -0.149011612E-7), (+0.596046448E-7, +0.119209290E-6), (+0.596046448E-7, +0.596046448E-7), (+0.238418579E-6, +0.00000000), (-0.596046448E-7, -0.894069672E-7), (-0.119209290E-6, +0.149011612E-6), (+0.119209290E-6, -0.447034836E-7), (+0.178813934E-6, -0.119209290E-6), (-0.596046448E-7, -0.178813934E-6), (+0.119209290E-6, -0.931322575E-7), (+0.00000000, -0.208616257E-6), (+0.00000000, -0.141561031E-6), (+0.596046448E-7, -0.208616257E-6), (-0.119209290E-6, +0.298023224E-7), (+0.596046448E-7, -0.208616257E-6), (-0.119209290E-6, +0.178813934E-6), (+0.00000000, +0.894069672E-7), (+0.00000000, +0.268220901E-6), (+0.00000000, +0.119209290E-6), (-0.596046448E-7, +0.268220901E-6), (-0.596046448E-7, +0.163912773E-6), (-0.298023224E-6, +0.275671482E-6), (+0.00000000, +0.149011612E-6), (+0.119209290E-6, +0.298023224E-7), (+0.119209290E-6, +0.00000000), (+0.00000000, +0.238418579E-6), (+0.119209290E-6, -0.894069672E-7), (-0.596046448E-7, +0.119209290E-6), (+0.119209290E-6, +0.596046448E-7), (-0.119209290E-6, +0.119209290E-6), (+0.00000000, +0.447034836E-7), (+0.596046448E-7, +0.968575478E-7), (+0.119209290E-6, +0.178813934E-6), (+0.00000000, +0.327825546E-6), (+0.119209290E-6, +0.596046448E-7), (+0.119209290E-6, +0.208616257E-6), (+0.596046448E-7, +0.327825546E-6), (-0.119209290E-6, +0.178813934E-6), (-0.596046448E-7, +0.327825546E-6), (+0.238418579E-6, -0.149011612E-7), (+0.238418579E-6, +0.596046448E-7), (-0.119209290E-6, +0.186264515E-6), (+0.298023224E-6, +0.298023224E-7), (-0.596046448E-7, +0.223517418E-7), (+0.178813934E-6, +0.268220901E-6), (-0.178813934E-6, +0.119209290E-6), (-0.119209290E-6, +0.119209290E-6)
228reltol = sqrt(epsilon(1._TKG))
229reltol
230+0.345266977E-3
231isClose(data, atad(1:size(data)), reltol = reltol)
232T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
233call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
234
235lenData = getUnifRand(5, 100)
236lenData
237+23
238data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
239data
240(+1.8521858523876373, +0.93951955709955626), (+1.2891752954718205, +0.28556571427236810), (+1.6604951665766139, +0.15462980353436162), (+1.3047238879741556, +0.32441546960124457), (+1.7699889219689044, +0.71894391186153095), (+1.0365752488032458, +0.77181973980306740), (+1.3156743434887823, +0.16435109826093153), (+1.0219944836788297, +0.12347288328286388), (+1.9832048787640018, +0.25799361422551559), (+1.3854227317039416, +0.94213972044738881), (+1.9981272662462468, +0.90940479042744549), (+1.7087905887126080, +0.88361743911412904), (+1.8371289107190556, +0.96994032279868714), (+1.1289465347078369, +0.46272485977218980), (+1.2839704590833727, +0.65557983379369411), (+1.2922734513600036, +0.50039356938596946), (+1.2820058566717358, +0.67623587596208168), (+1.7448846203629540, +0.76421266039122160), (+1.5075475735383788, +0.78348382269695871E-1), (+1.5444488993620502, +0.93821793001550136), (+1.3869535428940456, +0.36851245252899956), (+1.0509613030094913, +0.42259019695150424), (+1.3478859643352537, +0.68384144636548727)
241
242atad = getFFTR(getFFTF(data))
243atad = atad / size(atad)
244atad
245(+1.8521858523876378, +0.93951955709955626), (+1.2891752954718203, +0.28556571427236843), (+1.6604951665766137, +0.15462980353436179), (+1.3047238879741552, +0.32441546960124495), (+1.7699889219689042, +0.71894391186153095), (+1.0365752488032454, +0.77181973980306728), (+1.3156743434887821, +0.16435109826093158), (+1.0219944836788293, +0.12347288328286433), (+1.9832048787640020, +0.25799361422551537), (+1.3854227317039416, +0.94213972044738870), (+1.9981272662462464, +0.90940479042744538), (+1.7087905887126076, +0.88361743911412893), (+1.8371289107190554, +0.96994032279868669), (+1.1289465347078367, +0.46272485977218963), (+1.2839704590833723, +0.65557983379369389), (+1.2922734513600032, +0.50039356938596924), (+1.2820058566717361, +0.67623587596208168), (+1.7448846203629540, +0.76421266039122160), (+1.5075475735383785, +0.78348382269695815E-1), (+1.5444488993620502, +0.93821793001550113), (+1.3869535428940456, +0.36851245252899967), (+1.0509613030094911, +0.42259019695150374), (+1.3478859643352534, +0.68384144636548716), (+0.44408920985006262E-15, -0.29143354396410359E-15), (+0.22204460492503131E-15, +0.83266726846886741E-16), (+0.44408920985006262E-15, +0.38857805861880479E-15), (+0.22204460492503131E-15, -0.55511151231257827E-16), (+0.44408920985006262E-15, +0.27755575615628914E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.38857805861880479E-15), (+0.33306690738754696E-15, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.55511151231257827E-15)
246reltol = sqrt(epsilon(1._TKG))
247reltol
248+0.14901161193847656E-7
249isClose(data, atad(1:size(data)), reltol = reltol)
250T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
251call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
252
253lenData = getUnifRand(5, 100)
254lenData
255+15
256data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
257data
258(+1.43892947869011147479219733230011457, +0.222158149027789249718542630728345375), (+1.38341615703160691766710612587335236, +0.477993968523914579804982187106760832), (+1.05195075115667888032949830410834953, +0.221195905883090730017552542242314818), (+1.69053462500295546373235973023841015, +0.714424962271768670055424840370560656E-2), (+1.21813737669531137685809487355044195, +0.639307826684208918267430616987341663), (+1.28644105634003340058907870035575204, +0.806869240113118101348770785356033553), (+1.57580700832067618872661843015673591, +0.859955399995265220960468422690382263), (+1.45116887281105263284214929385240065, +0.742662420224012236572058582150916800E-3), (+1.59872410153955617955348726134317583, +0.130942644853946067227385940335914545), (+1.34595839460530860549542653336378049, +0.176168628453299486781478425751669475), (+1.84195554000189359120833619509239732, +0.894013219235698253931311532218896032), (+1.98138966945583265191965972168303694, +0.618498138059140921251201809155392774E-1), (+1.37244232838977251475685720551987654, +0.424289070472168114382171245689293630), (+1.75963383268891699967027519651194159, +0.897750605114645244059323681793864237), (+1.99939522991736697605637843780988712, +0.106204178994026230792846122890940186)
259
260atad = getFFTR(getFFTF(data))
261atad = atad / size(atad)
262atad
263(+1.43892947869011147479219733230011457, +0.222158149027789249718542630728345375), (+1.38341615703160691766710612587335255, +0.477993968523914579804982187106760736), (+1.05195075115667888032949830410834953, +0.221195905883090730017552542242314770), (+1.69053462500295546373235973023840996, +0.714424962271768670055424840370574498E-2), (+1.21813737669531137685809487355044175, +0.639307826684208918267430616987341663), (+1.28644105634003340058907870035575204, +0.806869240113118101348770785356033457), (+1.57580700832067618872661843015673572, +0.859955399995265220960468422690382359), (+1.45116887281105263284214929385240103, +0.742662420224012236572058582150724207E-3), (+1.59872410153955617955348726134317564, +0.130942644853946067227385940335914545), (+1.34595839460530860549542653336378049, +0.176168628453299486781478425751669403), (+1.84195554000189359120833619509239732, +0.894013219235698253931311532218895936), (+1.98138966945583265191965972168303694, +0.618498138059140921251201809155393316E-1), (+1.37244232838977251475685720551987634, +0.424289070472168114382171245689293630), (+1.75963383268891699967027519651194159, +0.897750605114645244059323681793864333), (+1.99939522991736697605637843780988692, +0.106204178994026230792846122890940042), (-0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34)
264reltol = sqrt(epsilon(1._TKG))
265reltol
266+0.138777878078144567552953958511352539E-16
267isClose(data, atad(1:size(data)), reltol = reltol)
268T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
269call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
270
271lenData = getUnifRand(5, 100)
272lenData
273+67
274data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
275data
276+1.94949889, +1.36165774, +1.89473128, +1.13890839, +1.74095488, +1.92782927, +1.06392360, +1.85263169, +1.91186619, +1.55997038, +1.68710768, +1.66098285, +1.79195976, +1.11062551, +1.11872160, +1.71869409, +1.61290443, +1.87154126, +1.60670519, +1.46603370, +1.93886733, +1.99120021, +1.92197406, +1.35593963, +1.70196366, +1.25257277, +1.61484098, +1.06274796, +1.71171761, +1.17389393, +1.71433187, +1.95398617, +1.18334997, +1.34408593, +1.18141937, +1.69897676, +1.37239385, +1.05304921, +1.89778674, +1.14221418, +1.29692090, +1.89637136, +1.79082191, +1.12393510, +1.15309763, +1.07554448, +1.18076980, +1.46958947, +1.76529169, +1.03325939, +1.13045096, +1.18159127, +1.59539640, +1.55746555, +1.65109634, +1.83911383, +1.92430830, +1.88421619, +1.59918976, +1.56854820, +1.65682650, +1.02631760, +1.60757375, +1.63585901, +1.40369129, +1.98848414, +1.64983010
277
278atad = getFFTR(getFFTF(data))
279atad = atad * 2 / size(atad)
280atad
281+1.94949865, +1.36165786, +1.89473128, +1.13890803, +1.74095464, +1.92782903, +1.06392348, +1.85263133, +1.91186631, +1.55997050, +1.68710780, +1.66098261, +1.79195952, +1.11062551, +1.11872160, +1.71869397, +1.61290407, +1.87154126, +1.60670495, +1.46603346, +1.93886721, +1.99120009, +1.92197394, +1.35593963, +1.70196366, +1.25257301, +1.61484098, +1.06274796, +1.71171761, +1.17389393, +1.71433163, +1.95398617, +1.18335009, +1.34408581, +1.18141925, +1.69897652, +1.37239408, +1.05304885, +1.89778662, +1.14221382, +1.29692101, +1.89637113, +1.79082179, +1.12393486, +1.15309763, +1.07554436, +1.18076968, +1.46958923, +1.76529169, +1.03325915, +1.13045073, +1.18159115, +1.59539628, +1.55746496, +1.65109611, +1.83911347, +1.92430806, +1.88421607, +1.59918928, +1.56854820, +1.65682638, +1.02631760, +1.60757375, +1.63585877, +1.40369129, +1.98848414, +1.64983010, +0.119209290E-6, +0.238418579E-6, +0.119209290E-6, +0.119209290E-6, +0.417232513E-6, +0.00000000, +0.00000000, +0.00000000, +0.238418579E-6, +0.178813934E-6, +0.298023224E-6, +0.119209290E-6, +0.178813934E-6, +0.298023224E-6, -0.596046448E-7, +0.298023224E-6, +0.596046448E-7, +0.238418579E-6, +0.119209290E-6, +0.00000000, -0.596046448E-7, +0.298023224E-6, -0.178813934E-6, +0.238418579E-6, +0.00000000, +0.00000000, +0.596046448E-7, +0.178813934E-6, -0.238418579E-6, -0.596046448E-7, +0.238418579E-6, +0.238418579E-6, +0.238418579E-6, -0.178813934E-6, +0.357627869E-6, -0.596046448E-7, +0.298023224E-6, -0.596046448E-7, +0.298023224E-6, +0.178813934E-6, +0.119209290E-6, -0.596046448E-7, +0.238418579E-6, -0.596046448E-7, +0.178813934E-6, +0.178813934E-6, +0.119209290E-6, +0.357627869E-6, +0.238418579E-6, +0.596046448E-7, +0.357627869E-6, +0.238418579E-6, +0.178813934E-6, +0.357627869E-6, +0.596046448E-7, +0.476837158E-6, +0.00000000, +0.119209290E-6, +0.596046448E-7, +0.178813934E-6, +0.596046448E-7
282reltol = sqrt(epsilon(1._TKG))
283reltol
284+0.345266977E-3
285isClose(data, atad(1:size(data)), reltol = reltol)
286T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
287call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
288
289lenData = getUnifRand(5, 100)
290lenData
291+77
292data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
293data
294+1.6831789534811614, +1.9559097962590390, +1.9189820164346165, +1.1402562590720906, +1.4308931860200649, +1.2909546973338337, +1.7500112738941711, +1.3504808040459766, +1.1537902585067772, +1.0797928922278746, +1.4321799202256951, +1.8285722136017477, +1.9827251668895429, +1.4024409170374854, +1.3108949554632945, +1.7949184560961853, +1.1952348931083450, +1.5651538184993485, +1.1086059976789151, +1.6067902023524434, +1.7856441709577693, +1.6094046395170729, +1.9790584193230916, +1.3128819859405283, +1.7481790690156447, +1.0365769084734378, +1.4977752823482327, +1.2874533359015559, +1.5401664029652897, +1.2945071091707889, +1.3954462540061716, +1.0832240779626146, +1.6322577206716637, +1.4873684049292977, +1.2734427109504587, +1.9695738328884311, +1.3224162401009010, +1.7737079528274693, +1.9855748636700543, +1.4336358177110471, +1.0883209133294804, +1.4208144993727849, +1.7047178415036321, +1.3404797996653830, +1.5128789260496334, +1.5544891501966358, +1.3023772681715557, +1.6436535433722876, +1.0494781407821072, +1.9171434498984667, +1.0180884644778725, +1.4724928463939118, +1.3865614096771897, +1.7976327754228554, +1.5470400789381535, +1.5161091185283353, +1.9076516940184840, +1.5848575132525189, +1.6243690522628182, +1.1639286805290490, +1.1787914725745829, +1.6358722720467300, +1.8925954139893080, +1.6052767406567627, +1.7309539593200933, +1.1486191445087137, +1.5760051558233219, +1.7901650580047299, +1.8754823959898266, +1.0875173194046268, +1.0813255916587572, +1.7038606448013107, +1.4065972989475530, +1.6754032691196792, +1.1899137744293677, +1.7118099018117396, +1.2173105008403478
295
296atad = getFFTR(getFFTF(data))
297atad = atad * 2 / size(atad)
298atad
299+1.6831789534811612, +1.9559097962590395, +1.9189820164346170, +1.1402562590720915, +1.4308931860200642, +1.2909546973338339, +1.7500112738941707, +1.3504808040459768, +1.1537902585067772, +1.0797928922278746, +1.4321799202256951, +1.8285722136017484, +1.9827251668895427, +1.4024409170374852, +1.3108949554632945, +1.7949184560961857, +1.1952348931083447, +1.5651538184993490, +1.1086059976789149, +1.6067902023524434, +1.7856441709577684, +1.6094046395170727, +1.9790584193230911, +1.3128819859405283, +1.7481790690156447, +1.0365769084734380, +1.4977752823482324, +1.2874533359015561, +1.5401664029652897, +1.2945071091707887, +1.3954462540061714, +1.0832240779626143, +1.6322577206716640, +1.4873684049292977, +1.2734427109504591, +1.9695738328884307, +1.3224162401009014, +1.7737079528274688, +1.9855748636700541, +1.4336358177110462, +1.0883209133294809, +1.4208144993727845, +1.7047178415036326, +1.3404797996653830, +1.5128789260496336, +1.5544891501966349, +1.3023772681715557, +1.6436535433722870, +1.0494781407821074, +1.9171434498984667, +1.0180884644778725, +1.4724928463939111, +1.3865614096771899, +1.7976327754228547, +1.5470400789381535, +1.5161091185283344, +1.9076516940184840, +1.5848575132525187, +1.6243690522628182, +1.1639286805290485, +1.1787914725745832, +1.6358722720467298, +1.8925954139893082, +1.6052767406567614, +1.7309539593200933, +1.1486191445087142, +1.5760051558233221, +1.7901650580047297, +1.8754823959898268, +1.0875173194046268, +1.0813255916587576, +1.7038606448013101, +1.4065972989475530, +1.6754032691196792, +1.1899137744293677, +1.7118099018117394, +1.2173105008403480, +0.0000000000000000, +0.99920072216264089E-15, -0.77715611723760958E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.44408920985006262E-15, -0.88817841970012523E-15, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.77715611723760958E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, -0.55511151231257827E-15, +0.55511151231257827E-15, +0.33306690738754696E-15, +0.99920072216264089E-15, -0.22204460492503131E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, -0.22204460492503131E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.0000000000000000, -0.11102230246251565E-15, -0.33306690738754696E-15, +0.55511151231257827E-15, +0.44408920985006262E-15, +0.44408920985006262E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, -0.11102230246251565E-15, +0.88817841970012523E-15, +0.22204460492503131E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.66613381477509392E-15, +0.11102230246251565E-15, +0.11102230246251565E-14
300reltol = sqrt(epsilon(1._TKG))
301reltol
302+0.14901161193847656E-7
303isClose(data, atad(1:size(data)), reltol = reltol)
304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
305call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
306
307lenData = getUnifRand(5, 100)
308lenData
309+43
310data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
311data
312+1.72290174249876579476648199082786000, +1.64778309201682139539020671419109589, +1.66234215645241761125100185009404455, +1.70490459281733805221901637814186414, +1.41724085961714118438172256739169243, +1.99965794537067845334516138703734618, +1.05999689213485227783549892517768250, +1.84174837044108196499026540152783822, +1.29298427374679079393138161607048626, +1.92708100134472330217098022580462729, +1.07351615915018795789913683246298929, +1.58761801624322511320033441643808263, +1.94861025474504729188235991985574644, +1.43853972119852934436061677186317416, +1.19726158281365696031390392169413123, +1.88729008189158539315077613228377042, +1.27279370234095327351431093853386236, +1.48560251066375217518228349693538782, +1.15248801939388892314209198987714403, +1.59588062518711728834444076924826668, +1.78658409160641582716547575104383974, +1.96968253985897788643881585625487354, +1.38759619588927187668098834691316613, +1.68027521132559532603789310180589517, +1.03464360092646451451583863045136664, +1.25909845100088559252460789712997814, +1.54069297925386563510679029560095976, +1.95640729057875666042543342029272046, +1.04998487148284583652453848531898469, +1.68879746869332748015570640563839816, +1.32213085574534523524739226650875925, +1.86880666325998312051789070416259630, +1.00963673512313736225701120431878381, +1.99573511842791500747986205923108425, +1.78721087792507129819099952086690834, +1.06846348339443741958588574841672254, +1.64163469308358441598783504949224274, +1.41321809202020651197978252172531310, +1.23043765406804289598114089069603281, +1.70862198337699835932175543179951525, +1.71627972153610464799284109905728752, +1.90407588990155586050140709474132392, +1.20071006274682439656424308570765390
313
314atad = getFFTR(getFFTF(data))
315atad = atad * 2 / size(atad)
316atad
317+1.72290174249876579476648199082786019, +1.64778309201682139539020671419109589, +1.66234215645241761125100185009404435, +1.70490459281733805221901637814186414, +1.41724085961714118438172256739169243, +1.99965794537067845334516138703734618, +1.05999689213485227783549892517768250, +1.84174837044108196499026540152783802, +1.29298427374679079393138161607048626, +1.92708100134472330217098022580462690, +1.07351615915018795789913683246298929, +1.58761801624322511320033441643808224, +1.94861025474504729188235991985574682, +1.43853972119852934436061677186317416, +1.19726158281365696031390392169413143, +1.88729008189158539315077613228377023, +1.27279370234095327351431093853386255, +1.48560251066375217518228349693538763, +1.15248801939388892314209198987714345, +1.59588062518711728834444076924826649, +1.78658409160641582716547575104383936, +1.96968253985897788643881585625487393, +1.38759619588927187668098834691316594, +1.68027521132559532603789310180589555, +1.03464360092646451451583863045136664, +1.25909845100088559252460789712997775, +1.54069297925386563510679029560095937, +1.95640729057875666042543342029272046, +1.04998487148284583652453848531898431, +1.68879746869332748015570640563839874, +1.32213085574534523524739226650875886, +1.86880666325998312051789070416259649, +1.00963673512313736225701120431878420, +1.99573511842791500747986205923108406, +1.78721087792507129819099952086690815, +1.06846348339443741958588574841672235, +1.64163469308358441598783504949224274, +1.41321809202020651197978252172531348, +1.23043765406804289598114089069603281, +1.70862198337699835932175543179951525, +1.71627972153610464799284109905728772, +1.90407588990155586050140709474132392, +1.20071006274682439656424308570765371, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, +0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, +0.577778983316170755916793382775478196E-33, +0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, -0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, +0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33
318reltol = sqrt(epsilon(1._TKG))
319reltol
320+0.138777878078144567552953958511352539E-16
321isClose(data, atad(1:size(data)), reltol = reltol)
322T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
323call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
324
325lenData = getUnifRand(5, 100)
326lenData
327+32
328data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
329data
330(+1.04019117, +0.444059312), (+1.95144248, +0.580220997), (+1.09144592, +0.854592979), (+1.00744247, +0.357789993E-1), (+1.78846586, +0.621751130), (+1.69438887, +0.681063592), (+1.71894503, +0.269150198), (+1.06105649, +0.729183257), (+1.28662372, +0.661314905), (+1.97296882, +0.438286126), (+1.56597471, +0.448712111), (+1.92595065, +0.347827673), (+1.06261373, +0.361493647), (+1.15880585, +0.683309495), (+1.43353844, +0.950683713), (+1.71828461, +0.761928558E-1), (+1.27068520, +0.535206795), (+1.45234096, +0.674258530), (+1.79293633, +0.787727416), (+1.81417704, +0.714302361), (+1.72808743, +0.797033250), (+1.42126691, +0.241648257), (+1.61374283, +0.269247472), (+1.64694822, +0.642016947), (+1.07873368, +0.200113297), (+1.14153373, +0.254228711), (+1.92445707, +0.535381496), (+1.70197725, +0.579680979), (+1.08507919, +0.406939447), (+1.61915898, +0.211304367), (+1.85173571, +0.404954612), (+1.86430681, +0.476200640)
331
332atad = getFFTR(getFFTF(data))
333atad = atad / size(atad)
334atad
335(+1.04019129, +0.444059283), (+1.95144248, +0.580220938), (+1.09144580, +0.854592919), (+1.00744236, +0.357790887E-1), (+1.78846586, +0.621751070), (+1.69438887, +0.681063652), (+1.71894491, +0.269150257), (+1.06105649, +0.729183316), (+1.28662384, +0.661314845), (+1.97296882, +0.438286036), (+1.56597459, +0.448712111), (+1.92595053, +0.347827673), (+1.06261384, +0.361493707), (+1.15880609, +0.683309436), (+1.43353820, +0.950683653), (+1.71828449, +0.761929154E-1), (+1.27068532, +0.535206795), (+1.45234108, +0.674258590), (+1.79293621, +0.787727475), (+1.81417692, +0.714302301), (+1.72808754, +0.797033191), (+1.42126703, +0.241648287), (+1.61374271, +0.269247532), (+1.64694822, +0.642017007), (+1.07873380, +0.200113267), (+1.14153385, +0.254228741), (+1.92445695, +0.535381556), (+1.70197701, +0.579681039), (+1.08507931, +0.406939507), (+1.61915898, +0.211304456), (+1.85173559, +0.404954612), (+1.86430681, +0.476200700)
336reltol = sqrt(epsilon(1._TKG))
337reltol
338+0.345266977E-3
339isClose(data, atad(1:size(data)), reltol = reltol)
340T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
341call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
342
343lenData = getUnifRand(5, 100)
344lenData
345+26
346data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
347data
348(+1.7278203044075475, +0.67125626827058560), (+1.7049921052819710, +0.64991505186890075), (+1.1912904986598987, +0.84463359493988965), (+1.5538490566799779, +0.75816508567833718), (+1.8838669642341439, +0.18275291763121282), (+1.3555713501115081, +0.99944581854216485), (+1.7813298594079168, +0.36306673911015563), (+1.3752435718827769, +0.45906862703057483), (+1.6733554294661883, +0.27104044186549825), (+1.4102060161221781, +0.10158076910153191), (+1.4203570329013393, +0.99713024414489515), (+1.8746582784793981, +0.67673584557254873), (+1.8179588114876117, +0.32669751856969709), (+1.1556295074594152, +0.73207139674007782), (+1.0640804496077896, +0.46355003755753699), (+1.4029180355862698, +0.48217793076604143), (+1.1325781197283797, +0.53529635572872392), (+1.1358429190640571, +0.79597297006632550), (+1.4724426010496452, +0.97287930002213985), (+1.4740775335348562, +0.71559161019538875), (+1.2987201667845247, +0.95988169735326179), (+1.7878490451419826, +0.60128865188482483E-1), (+1.7113495158819794, +0.74935620491631050), (+1.5452679702373091, +0.81142351085530051), (+1.6572695918627647, +0.95433112079661930), (+1.7947139745734180, +0.57486781972131373)
349
350atad = getFFTR(getFFTF(data))
351atad = atad / size(atad)
352atad
353(+1.7278203044075475, +0.67125626827058560), (+1.7049921052819714, +0.64991505186890097), (+1.1912904986598984, +0.84463359493988976), (+1.5538490566799779, +0.75816508567833751), (+1.8838669642341435, +0.18275291763121293), (+1.3555713501115079, +0.99944581854216463), (+1.7813298594079161, +0.36306673911015575), (+1.3752435718827769, +0.45906862703057472), (+1.6733554294661883, +0.27104044186549842), (+1.4102060161221783, +0.10158076910153202), (+1.4203570329013391, +0.99713024414489504), (+1.8746582784793979, +0.67673584557254851), (+1.8179588114876113, +0.32669751856969698), (+1.1556295074594152, +0.73207139674007760), (+1.0640804496077894, +0.46355003755753676), (+1.4029180355862696, +0.48217793076604143), (+1.1325781197283797, +0.53529635572872381), (+1.1358429190640575, +0.79597297006632539), (+1.4724426010496450, +0.97287930002213985), (+1.4740775335348564, +0.71559161019538875), (+1.2987201667845247, +0.95988169735326168), (+1.7878490451419824, +0.60128865188482428E-1), (+1.7113495158819789, +0.74935620491631016), (+1.5452679702373091, +0.81142351085530040), (+1.6572695918627649, +0.95433112079661941), (+1.7947139745734182, +0.57486781972131351), (+0.33306690738754696E-15, +0.16653345369377348E-15), (+0.33306690738754696E-15, +0.0000000000000000), (+0.44408920985006262E-15, +0.30531133177191805E-15), (+0.66613381477509392E-15, +0.27755575615628914E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.77715611723760958E-15, +0.55511151231257827E-15)
354reltol = sqrt(epsilon(1._TKG))
355reltol
356+0.14901161193847656E-7
357isClose(data, atad(1:size(data)), reltol = reltol)
358T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
359call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
360
361lenData = getUnifRand(5, 100)
362lenData
363+33
364data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
365data
366(+1.70498743522571570600175039145909116, +0.133697125274620987470233938918285036), (+1.53484189348794360324261421657297698, +0.519465246976204458636607703496487267), (+1.31186997603644485871368581643169293, +0.812224243577600280906413356574357612), (+1.14170546877825947803043712854535900, +0.409229718972625242404929463127643441), (+1.54898933865769762053674231938430807, +0.692969043140793268026995087852885684), (+1.92004255032464203738227298388782677, +0.215549688156912101720056329009922391E-1), (+1.67924071314260094950420427557466412, +0.515962415396325197436312691223726030), (+1.96959222563181622157539294188412726, +0.131573512343812839970095401013190603), (+1.89045887232054572521002985753047795, +0.589982392732991669957717194114204021), (+1.81013493973397820487075215904802153, +0.432107903956450891422208185660778018), (+1.48974523808283593814651673147468956, +0.724804793503724275104361734274422980), (+1.60111137125066602507338988244146492, +0.971709474526610515792396416170887070), (+1.11696586685688999026046768583889090, +0.942562647283794677018282786513744538), (+1.80286611572539108125644818738258528, +0.673036624382970983418406022825936122), (+1.96442860179716510075362886175345252, +0.115182019307956071177412612368099087), (+1.07345228329462006059896079400598863, +0.686764587401409808041586549312564700), (+1.29375142820226031283181401135471197, +0.484727207407655103098334831300561200), (+1.16054552417291233279775190219988103, +0.304594745394509816103407874703000266E-1), (+1.11508581801783267310398094325412707, +0.426614803192603139831846448592107267), (+1.51457043562144108264340490142483636, +0.358243865272405224777833406796747412), (+1.63709163720979763633453999954155252, +0.244235157219425882318123583027704338), (+1.99639784048393268713986218859824855, +0.655499395222181831692108768310364073), (+1.78551079049638813225609675668351428, +0.175971691077433804424943916698940114), (+1.02014843920268798603669233610299646, +0.275584333125019053794784527113598399), (+1.77407919336764290246414285633219715, +0.492297478821532092571640765351541505), (+1.56546327639248890085646943274081255, +0.373185314934251196330959121736866436), (+1.67328447466320891416378824247707188, +0.958635994103029678596634662152500945), (+1.84743959648645990082233099982492259, +0.576824372510945767761936100224419192), (+1.13628148585630297716084349682469306, +0.320634845349789893763301999985303708), (+1.68177682291431461759225122021357930, +0.216992031750390465456385772048442477), (+1.81370957161944172926422046217264359, +0.361879574609767366190717637063026173), (+1.42854913771831275658486773184927777, +0.865974562756530636425926382586410323E-1), (+1.71976035914762458186839163160404946, +0.438963822758366827382258497268793448)
367
368atad = getFFTR(getFFTF(data))
369atad = atad / size(atad)
370atad
371(+1.70498743522571570600175039145909116, +0.133697125274620987470233938918285204), (+1.53484189348794360324261421657297698, +0.519465246976204458636607703496487170), (+1.31186997603644485871368581643169293, +0.812224243577600280906413356574357708), (+1.14170546877825947803043712854535880, +0.409229718972625242404929463127643441), (+1.54898933865769762053674231938430846, +0.692969043140793268026995087852885780), (+1.92004255032464203738227298388782735, +0.215549688156912101720056329009919984E-1), (+1.67924071314260094950420427557466431, +0.515962415396325197436312691223725741), (+1.96959222563181622157539294188412726, +0.131573512343812839970095401013190362), (+1.89045887232054572521002985753047756, +0.589982392732991669957717194114204117), (+1.81013493973397820487075215904802153, +0.432107903956450891422208185660777921), (+1.48974523808283593814651673147468937, +0.724804793503724275104361734274422788), (+1.60111137125066602507338988244146454, +0.971709474526610515792396416170886974), (+1.11696586685688999026046768583889110, +0.942562647283794677018282786513744731), (+1.80286611572539108125644818738258547, +0.673036624382970983418406022825936411), (+1.96442860179716510075362886175345291, +0.115182019307956071177412612368099376), (+1.07345228329462006059896079400598844, +0.686764587401409808041586549312564892), (+1.29375142820226031283181401135471197, +0.484727207407655103098334831300561200), (+1.16054552417291233279775190219988103, +0.304594745394509816103407874703001169E-1), (+1.11508581801783267310398094325412707, +0.426614803192603139831846448592107027), (+1.51457043562144108264340490142483617, +0.358243865272405224777833406796747316), (+1.63709163720979763633453999954155271, +0.244235157219425882318123583027704266), (+1.99639784048393268713986218859824874, +0.655499395222181831692108768310364362), (+1.78551079049638813225609675668351467, +0.175971691077433804424943916698939898), (+1.02014843920268798603669233610299607, +0.275584333125019053794784527113598447), (+1.77407919336764290246414285633219696, +0.492297478821532092571640765351541120), (+1.56546327639248890085646943274081255, +0.373185314934251196330959121736866629), (+1.67328447466320891416378824247707188, +0.958635994103029678596634662152500464), (+1.84743959648645990082233099982492259, +0.576824372510945767761936100224419000), (+1.13628148585630297716084349682469325, +0.320634845349789893763301999985303612), (+1.68177682291431461759225122021357910, +0.216992031750390465456385772048442958), (+1.81370957161944172926422046217264378, +0.361879574609767366190717637063026077), (+1.42854913771831275658486773184927777, +0.865974562756530636425926382586410444E-1), (+1.71976035914762458186839163160404965, +0.438963822758366827382258497268793255), (-0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (+0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-33), (+0.00000000000000000000000000000000000, +0.240741243048404481631997242823115915E-34), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (-0.577778983316170755916793382775478196E-33, +0.144444745829042688979198345693869549E-33), (-0.192592994438723585305597794258492732E-33, +0.144444745829042688979198345693869549E-33), (-0.481482486096808963263994485646231830E-33, +0.240741243048404481631997242823115915E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, +0.168518870133883137142398069976181140E-33), (+0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (+0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (-0.481482486096808963263994485646231830E-33, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33), (-0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, +0.240741243048404481631997242823115915E-34), (-0.962964972193617926527988971292463659E-34, -0.138426214752832576938398414623291651E-33), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.240741243048404481631997242823115915E-34), (+0.00000000000000000000000000000000000, -0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, -0.337037740267766274284796139952362281E-33), (-0.385185988877447170611195588516985464E-33, +0.722223729145213444895991728469347744E-34), (-0.962964972193617926527988971292463659E-34, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33), (-0.962964972193617926527988971292463659E-34, -0.120370621524202240815998621411557957E-33), (-0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, +0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34), (+0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-33), (-0.962964972193617926527988971292463659E-34, -0.240741243048404481631997242823115915E-34), (-0.385185988877447170611195588516985464E-33, -0.108333559371782016734398759270402162E-33)
372reltol = sqrt(epsilon(1._TKG))
373reltol
374+0.138777878078144567552953958511352539E-16
375isClose(data, atad(1:size(data)), reltol = reltol)
376T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
377call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
378
379lenData = getUnifRand(5, 100)
380lenData
381+38
382data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
383data
384+1.11477828, +1.48705816, +1.63354647, +1.50537300, +1.57733488, +1.36002922, +1.28960180, +1.61076105, +1.75934315, +1.72128093, +1.99003386, +1.66859019, +1.68313611, +1.57274806, +1.41214895, +1.48938417, +1.85470772, +1.01661670, +1.30467451, +1.87508082, +1.22188520, +1.83231711, +1.70706058, +1.93259323, +1.15904188, +1.14085722, +1.62720704, +1.77287841, +1.29108310, +1.61790514, +1.41608715, +1.72858632, +1.19639802, +1.85780835, +1.05893540, +1.98406363, +1.75056827, +1.51044464
385
386atad = getFFTR(getFFTF(data))
387atad = atad * 2 / size(atad)
388atad
389+1.11477828, +1.48705804, +1.63354635, +1.50537276, +1.57733500, +1.36002910, +1.28960180, +1.61076069, +1.75934279, +1.72128081, +1.99003410, +1.66859019, +1.68313599, +1.57274806, +1.41214919, +1.48938394, +1.85470784, +1.01661658, +1.30467486, +1.87508070, +1.22188520, +1.83231699, +1.70706081, +1.93259335, +1.15904188, +1.14085722, +1.62720704, +1.77287841, +1.29108310, +1.61790502, +1.41608739, +1.72858620, +1.19639802, +1.85780823, +1.05893564, +1.98406363, +1.75056827, +1.51044452, -0.596046448E-7, +0.596046448E-7, +0.119209290E-6, +0.596046448E-7, -0.596046448E-7, +0.238418579E-6, +0.238418579E-6, +0.119209290E-6, -0.596046448E-7, +0.298023224E-6, -0.119209290E-6, +0.596046448E-7, -0.596046448E-7, +0.119209290E-6, +0.596046448E-7, +0.119209290E-6, -0.178813934E-6, -0.119209290E-6, +0.596046448E-7, +0.119209290E-6, +0.596046448E-7, +0.298023224E-6, +0.178813934E-6, +0.119209290E-6, -0.596046448E-7, +0.596046448E-7
390reltol = sqrt(epsilon(1._TKG))
391reltol
392+0.345266977E-3
393isClose(data, atad(1:size(data)), reltol = reltol)
394T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
395call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
396
397lenData = getUnifRand(5, 100)
398lenData
399+94
400data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
401data
402+1.2720962438630754, +1.6984693520300884, +1.7807625591740783, +1.7849327011344025, +1.2834232151145410, +1.6227828271962119, +1.9451612534881593, +1.5510712833243641, +1.2180879377511129, +1.4914339380769965, +1.2884426171979029, +1.3890413160289454, +1.4508395993750436, +1.2542579526505486, +1.8966978996113824, +1.5190036568582277, +1.9021988634575837, +1.9077186261785521, +1.3138407405084269, +1.3268855064346941, +1.4496366023802418, +1.2631461976520910, +1.5451317935299662, +1.3838975249101402, +1.3134769755434821, +1.1408773998778829, +1.1222495490393749, +1.7420004240324998, +1.7163674205697932, +1.5240564727420431, +1.8172845484977329, +1.3940686730300254, +1.8897359174337591, +1.3572760882220156, +1.3180157134206116, +1.0114311760285151, +1.3945380051754301, +1.2764268289171832, +1.3204918461373796, +1.4121844608198262, +1.1414231789813902, +1.9311641450078341, +1.5729494480310255, +1.0792606161383584, +1.4452264199273377, +1.0713335057868791, +1.1854865195421314, +1.3894986458856164, +1.4068967291021419, +1.6462586714377199, +1.1400236192785926, +1.6062439630834726, +1.1126712065064632, +1.0947174506611308, +1.1895594864473691, +1.1439506626319083, +1.7655704184688876, +1.9927858601038331, +1.0108196618343688, +1.7669187615997499, +1.2291118543683135, +1.2011108313360210, +1.8414568959449289, +1.5013585325528713, +1.0893332555290374, +1.9924706316193210, +1.5094150049361423, +1.7741530273134711, +1.6775702066860603, +1.8061599326336468, +1.0854440841993078, +1.6310220365334311, +1.5251397304935574, +1.9344334124248519, +1.0078498364268784, +1.8368893901427916, +1.3223127903720158, +1.1772776614765263, +1.0791180879524731, +1.2456527590492601, +1.7680467578189036, +1.2543598373262088, +1.9761856426080096, +1.0166106041998502, +1.3342765039239981, +1.0998465270447202, +1.6307532486681886, +1.4567925644969795, +1.9728000809406820, +1.1077302207300241, +1.1492000761581838, +1.9895546283461965, +1.2611504732718148, +1.5147851860228410
403
404atad = getFFTR(getFFTF(data))
405atad = atad * 2 / size(atad)
406atad
407+1.2720962438630752, +1.6984693520300884, +1.7807625591740783, +1.7849327011344027, +1.2834232151145406, +1.6227828271962121, +1.9451612534881582, +1.5510712833243645, +1.2180879377511127, +1.4914339380769965, +1.2884426171979029, +1.3890413160289452, +1.4508395993750429, +1.2542579526505484, +1.8966978996113817, +1.5190036568582277, +1.9021988634575833, +1.9077186261785524, +1.3138407405084267, +1.3268855064346943, +1.4496366023802412, +1.2631461976520910, +1.5451317935299658, +1.3838975249101402, +1.3134769755434814, +1.1408773998778836, +1.1222495490393745, +1.7420004240324998, +1.7163674205697927, +1.5240564727420431, +1.8172845484977320, +1.3940686730300256, +1.8897359174337591, +1.3572760882220156, +1.3180157134206114, +1.0114311760285146, +1.3945380051754299, +1.2764268289171830, +1.3204918461373794, +1.4121844608198260, +1.1414231789813902, +1.9311641450078343, +1.5729494480310255, +1.0792606161383584, +1.4452264199273372, +1.0713335057868791, +1.1854865195421311, +1.3894986458856158, +1.4068967291021419, +1.6462586714377196, +1.1400236192785924, +1.6062439630834722, +1.1126712065064632, +1.0947174506611306, +1.1895594864473686, +1.1439506626319078, +1.7655704184688878, +1.9927858601038326, +1.0108196618343686, +1.7669187615997495, +1.2291118543683137, +1.2011108313360208, +1.8414568959449285, +1.5013585325528704, +1.0893332555290371, +1.9924706316193208, +1.5094150049361419, +1.7741530273134709, +1.6775702066860598, +1.8061599326336466, +1.0854440841993078, +1.6310220365334309, +1.5251397304935577, +1.9344334124248517, +1.0078498364268782, +1.8368893901427914, +1.3223127903720153, +1.1772776614765259, +1.0791180879524729, +1.2456527590492599, +1.7680467578189034, +1.2543598373262086, +1.9761856426080098, +1.0166106041998499, +1.3342765039239981, +1.0998465270447197, +1.6307532486681886, +1.4567925644969784, +1.9728000809406818, +1.1077302207300244, +1.1492000761581833, +1.9895546283461960, +1.2611504732718148, +1.5147851860228405, +0.44408920985006262E-15, -0.66613381477509392E-15, -0.33306690738754696E-15, +0.33306690738754696E-15, -0.33306690738754696E-15, -0.66613381477509392E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.11102230246251565E-15, -0.22204460492503131E-15, -0.11102230246251565E-15, -0.22204460492503131E-15, +0.0000000000000000, -0.22204460492503131E-15, -0.22204460492503131E-15, +0.44408920985006262E-15, -0.11102230246251565E-15, +0.11102230246251565E-15, -0.22204460492503131E-15, +0.33306690738754696E-15, +0.0000000000000000, -0.33306690738754696E-15, -0.11102230246251565E-15, +0.66613381477509392E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.0000000000000000, +0.77715611723760958E-15, -0.44408920985006262E-15, +0.99920072216264089E-15
408reltol = sqrt(epsilon(1._TKG))
409reltol
410+0.14901161193847656E-7
411isClose(data, atad(1:size(data)), reltol = reltol)
412T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
413call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
414
415lenData = getUnifRand(5, 100)
416lenData
417+13
418data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
419data
420+1.59647854806429848280704534010368427, +1.25560860956265780969874212310126581, +1.54380132875291793763807332507625467, +1.38893871966163411377280416467115739, +1.51611613157084270223600267628713135, +1.51490073535043350487868940368397770, +1.55918697784890520641978100411392268, +1.16993806982510606796680635732686108, +1.31317172099587123582937631181687018, +1.42603147823681230927655647846269362, +1.76307308000572023587300798468610910, +1.04962785735629860161115626169918276, +1.97773951097710485390061289048474928
421
422atad = getFFTR(getFFTF(data))
423atad = atad * 2 / size(atad)
424atad
425+1.59647854806429848280704534010368427, +1.25560860956265780969874212310126581, +1.54380132875291793763807332507625486, +1.38893871966163411377280416467115759, +1.51611613157084270223600267628713135, +1.51490073535043350487868940368397770, +1.55918697784890520641978100411392287, +1.16993806982510606796680635732686108, +1.31317172099587123582937631181687018, +1.42603147823681230927655647846269362, +1.76307308000572023587300798468610949, +1.04962785735629860161115626169918295, +1.97773951097710485390061289048474928, -0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33
426reltol = sqrt(epsilon(1._TKG))
427reltol
428+0.138777878078144567552953958511352539E-16
429isClose(data, atad(1:size(data)), reltol = reltol)
430T, T, T, T, T, T, T, T, T, T, T, T, T
431call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
432
433lenData = getUnifRand(5, 100)
434lenData
435+51
436data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
437data
438(+1.42203510, +0.959725797), (+1.86666691, +0.542399943), (+1.43187952, +0.793038070), (+1.56547594, +0.257553935), (+1.85895610, +0.522386789), (+1.86146903, +0.544164896), (+1.60419154, +0.770968914), (+1.65794528, +0.668529987), (+1.49111223, +0.653100908), (+1.91823924, +0.991625488), (+1.78004348, +0.994005024), (+1.93596220, +0.496143222), (+1.36707044, +0.215871274), (+1.95901060, +0.507721901E-1), (+1.27912807, +0.967899203), (+1.07835710, +0.514115095E-1), (+1.34191394, +0.249450326), (+1.68993235, +0.721394658), (+1.39023745, +0.284350336), (+1.63260543, +0.231620371), (+1.77936351, +0.609210074), (+1.05865073, +0.270047784), (+1.12005830, +0.266942739), (+1.59964323, +0.493148327), (+1.33585382, +0.402242422), (+1.08249402, +0.243852437), (+1.53990984, +0.338833272), (+1.59557390, +0.729194999), (+1.80289781, +0.166355610), (+1.56261754, +0.697698593), (+1.37230301, +0.903806090E-1), (+1.67050791, +0.811217427E-1), (+1.23306799, +0.134467840), (+1.96164227, +0.569912910), (+1.94993031, +0.312562644), (+1.81928945, +0.415778875), (+1.97300792, +0.152578354), (+1.02232242, +0.310000896), (+1.59096456, +0.596734464), (+1.25265121, +0.335400879), (+1.42055583, +0.224750996), (+1.95357597, +0.168826997), (+1.83354712, +0.607288480E-1), (+1.84809721, +0.465011597E-2), (+1.26898527, +0.612833261), (+1.92648506, +0.835777521E-1), (+1.86453748, +0.378826201), (+1.18974972, +0.313873172), (+1.65752089, +0.472193897), (+1.45789587, +0.655932903), (+1.15384793, +0.725732803)
439
440atad = getFFTR(getFFTF(data))
441atad = atad / size(atad)
442atad
443(+1.42203510, +0.959725857), (+1.86666679, +0.542399943), (+1.43187952, +0.793038011), (+1.56547570, +0.257553905), (+1.85895622, +0.522386849), (+1.86146891, +0.544164896), (+1.60419142, +0.770968854), (+1.65794516, +0.668529928), (+1.49111235, +0.653100967), (+1.91823924, +0.991625547), (+1.78004360, +0.994004905), (+1.93596220, +0.496143311), (+1.36707067, +0.215871379), (+1.95901072, +0.507723540E-1), (+1.27912819, +0.967899144), (+1.07835734, +0.514116287E-1), (+1.34191406, +0.249450222), (+1.68993223, +0.721394539), (+1.39023769, +0.284350514), (+1.63260508, +0.231620267), (+1.77936375, +0.609210014), (+1.05865085, +0.270047784), (+1.12005830, +0.266942799), (+1.59964323, +0.493148208), (+1.33585393, +0.402242422), (+1.08249402, +0.243852526), (+1.53990960, +0.338833243), (+1.59557378, +0.729194880), (+1.80289793, +0.166355699), (+1.56261742, +0.697698593), (+1.37230301, +0.903806761E-1), (+1.67050791, +0.811217949E-1), (+1.23306811, +0.134467870), (+1.96164227, +0.569912970), (+1.94993019, +0.312562585), (+1.81928945, +0.415778726), (+1.97300804, +0.152578428), (+1.02232254, +0.310000896), (+1.59096467, +0.596734464), (+1.25265145, +0.335400879), (+1.42055595, +0.224750981), (+1.95357597, +0.168827057), (+1.83354712, +0.607288480E-1), (+1.84809732, +0.465002656E-2), (+1.26898527, +0.612833321), (+1.92648494, +0.835777670E-1), (+1.86453736, +0.378826320), (+1.18974984, +0.313873202), (+1.65752089, +0.472193897), (+1.45789587, +0.655932784), (+1.15384829, +0.725732684), (+0.417232513E-6, +0.342726707E-6), (+0.119209290E-6, +0.00000000), (+0.238418579E-6, -0.447034836E-7), (+0.178813934E-6, +0.596046448E-7), (+0.238418579E-6, +0.163912773E-6), (+0.238418579E-6, -0.447034836E-7), (+0.238418579E-6, -0.298023224E-7), (+0.298023224E-6, +0.298023224E-7), (+0.238418579E-6, +0.119209290E-6), (+0.357627869E-6, -0.178813934E-6), (+0.357627869E-6, -0.178813934E-6), (+0.178813934E-6, -0.670552254E-7), (+0.178813934E-6, -0.223517418E-7)
444reltol = sqrt(epsilon(1._TKG))
445reltol
446+0.345266977E-3
447isClose(data, atad(1:size(data)), reltol = reltol)
448T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
449call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
450
451lenData = getUnifRand(5, 100)
452lenData
453+28
454data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
455data
456(+1.1981059539009302, +0.88096707085824477), (+1.5915612084002273, +0.44738701566120409), (+1.1428679674237503, +0.48877149386384056), (+1.5322670515727266, +0.68198071598439691), (+1.2153410455669158, +0.96899386418974875), (+1.8745597640410905, +0.11249054015684279), (+1.5560043289641903, +0.40991860302277283), (+1.6105538403221231, +0.34951678979049805), (+1.3680483550228366, +0.35787966574621866), (+1.4572682950622800, +0.39002304701087787), (+1.6916305301132903, +0.55398427077126589), (+1.4239488821822242, +0.11678747518771193), (+1.1779219458768690, +0.47105504937629150), (+1.5011721154735056, +0.52898068044442281), (+1.6168731596569597, +0.13902980425017031E-1), (+1.6759023310982029, +0.29806777667010687), (+1.0597026186583585, +0.56693617920784511), (+1.8397811841602936, +0.17999453530407028), (+1.1279290045962820, +0.30557352656502090), (+1.7176626337239744, +0.69874944657126103), (+1.5967049555047557, +0.35355796273652218), (+1.6463873823328932, +0.86421190531506298), (+1.5973677957974748, +0.12568778527000435), (+1.9191274983838453, +0.10469186988228962E-2), (+1.1415312679739142, +0.28431031983809063), (+1.2756243397501881, +0.85474038554065279), (+1.4727245135619866, +0.76068286047380540), (+1.0881633262009225, +0.14544201144801461)
457
458atad = getFFTR(getFFTF(data))
459atad = atad / size(atad)
460atad
461(+1.1981059539009302, +0.88096707085824477), (+1.5915612084002271, +0.44738701566120415), (+1.1428679674237501, +0.48877149386384050), (+1.5322670515727266, +0.68198071598439702), (+1.2153410455669156, +0.96899386418974864), (+1.8745597640410900, +0.11249054015684301), (+1.5560043289641903, +0.40991860302277289), (+1.6105538403221229, +0.34951678979049772), (+1.3680483550228364, +0.35787966574621866), (+1.4572682950622797, +0.39002304701087792), (+1.6916305301132901, +0.55398427077126589), (+1.4239488821822239, +0.11678747518771204), (+1.1779219458768690, +0.47105504937629145), (+1.5011721154735054, +0.52898068044442259), (+1.6168731596569592, +0.13902980425016948E-1), (+1.6759023310982024, +0.29806777667010687), (+1.0597026186583585, +0.56693617920784500), (+1.8397811841602933, +0.17999453530407034), (+1.1279290045962818, +0.30557352656502085), (+1.7176626337239744, +0.69874944657126103), (+1.5967049555047557, +0.35355796273652201), (+1.6463873823328927, +0.86421190531506253), (+1.5973677957974748, +0.12568778527000418), (+1.9191274983838449, +0.10469186988230073E-2), (+1.1415312679739142, +0.28431031983809074), (+1.2756243397501879, +0.85474038554065257), (+1.4727245135619866, +0.76068286047380518), (+1.0881633262009225, +0.14544201144801427), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.55511151231257827E-15, +0.22204460492503131E-15), (+0.55511151231257827E-15, +0.13877787807814457E-15), (+0.88817841970012523E-15, +0.30531133177191805E-15)
462reltol = sqrt(epsilon(1._TKG))
463reltol
464+0.14901161193847656E-7
465isClose(data, atad(1:size(data)), reltol = reltol)
466T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
467call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
468
469lenData = getUnifRand(5, 100)
470lenData
471+74
472data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)
473data
474(+1.87278303734504560441167870854066774, +0.425074847173661669519634755554242914), (+1.30028646108355570158903705476985114, +0.153104341067959596544792913035726559), (+1.33432592321536488475213503399124941, +0.145587534873423421809916927116176131), (+1.16385746481809110546662168686763374, +0.264108923664630734401017554962152384), (+1.33864972770917018373009231127690056, +0.376108459378279056763861170019278228), (+1.68360528217942618579373174088565829, +0.126469818107141747709688812968951740), (+1.27793686717952539569611643624961996, +0.472207305998197298608456884679406945), (+1.58661943199217870917900390201725769, +0.372816401519302062509914938385926316), (+1.95444205616836716045621671676739573, +0.383729667221709673385876804202288409), (+1.86412615814844921194979686805426764, +0.796910312274045969646434592646062859), (+1.33061773829538046481752698503349997, +0.417827329516008656174573974067931554), (+1.78141242297282577265511077461795439, +0.688641603942904460998616540612641027), (+1.29132317229329286951873332331717520, +0.999546082284657632526837485748457751E-2), (+1.60333547137324784334172550924314949, +0.601073350122186993319979825413407748), (+1.53036593697650779338509586438521326, +0.798992946508209959389251365000147390E-1), (+1.80337187104790941125991106994930162, +0.533053297204249713759644880445959535), (+1.61967193751122350317237584417130200, +0.838046961821184332725441231751621618), (+1.35291580023336180221623000266544225, +0.687598074583786665341546327286162238), (+1.14590703262771476490950217949444135, +0.173635770446764273405763131157658195E-1), (+1.94071588204283258397218403849409711, +0.440179785684770238616785859003388332), (+1.77211049240779623411464242976478338, +0.690952573569175480608238671387690676), (+1.86820748555441610278147512516530448, +0.496115365609924877716665724600091926), (+1.35961920517107606503759271448855865, +0.602702833563705922759503802850416089), (+1.68212910428058472319476016472141346, +0.318226320052239268208636151382144156), (+1.46720484350740171241246639864331509, +0.423199693184066887973358635648008053), (+1.22130525478704294941264473825876884, +0.800521252263613078913390655778701098), (+1.66822482599300349596211650753867026, +0.832269654554937235201704289905449555), (+1.11237918889241308106818296029604498, +0.333324966354758680792395969337675862), (+1.90031842884619921329301630959548175, +0.543046404608878191072796933314421126E-1), (+1.53047477769276796535262827027723109, +0.779509330610971477699220422137274968E-1), (+1.17300780921436232673879541398334224, +0.725151351924318914711449540112573039), (+1.00121719841012642022867790061556499, +0.924570956784837288586582542013090903), (+1.17707970922148568746446476351751109, +0.138138990575819283984532201113471022), (+1.70879768278373330886720195847052134, +0.123383092758142573850141170757189578E-1), (+1.28063597456812357646034964914171608, +0.125490437223184071718070535614821236E-1), 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475
476atad = getFFTR(getFFTF(data))
477atad = atad / size(atad)
478atad
479(+1.87278303734504560441167870854066774, +0.425074847173661669519634755554242817), (+1.30028646108355570158903705476985114, +0.153104341067959596544792913035726270), (+1.33432592321536488475213503399124922, +0.145587534873423421809916927116176107), (+1.16385746481809110546662168686763374, +0.264108923664630734401017554962152191), (+1.33864972770917018373009231127690056, +0.376108459378279056763861170019277940), (+1.68360528217942618579373174088565848, +0.126469818107141747709688812968951427), (+1.27793686717952539569611643624961958, +0.472207305998197298608456884679406752), (+1.58661943199217870917900390201725769, +0.372816401519302062509914938385925883), (+1.95444205616836716045621671676739592, +0.383729667221709673385876804202288409), (+1.86412615814844921194979686805426822, +0.796910312274045969646434592646063051), (+1.33061773829538046481752698503350035, +0.417827329516008656174573974067931554), (+1.78141242297282577265511077461795517, +0.688641603942904460998616540612641027), 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(-0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-34), (+0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34), (-0.385185988877447170611195588516985464E-33, +0.264815367353244929795196967105427506E-33), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.168518870133883137142398069976181140E-33), (-0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (-0.192592994438723585305597794258492732E-33, +0.433334237487128066937595037081608647E-33), (-0.192592994438723585305597794258492732E-33, -0.120370621524202240815998621411557957E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33), (-0.288889491658085377958396691387739098E-33, -0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.168518870133883137142398069976181140E-33), (-0.481482486096808963263994485646231830E-33, +0.210648587667353921427997587470226425E-33), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000), (-0.962964972193617926527988971292463659E-34, -0.120370621524202240815998621411557957E-33), (-0.192592994438723585305597794258492732E-33, +0.300926553810505602039996553528894894E-34), (-0.962964972193617926527988971292463659E-34, -0.902779661431516806119989660586684681E-34), (-0.385185988877447170611195588516985464E-33, -0.168518870133883137142398069976181140E-33), (+0.00000000000000000000000000000000000, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, +0.120370621524202240815998621411557957E-33), (-0.385185988877447170611195588516985464E-33, -0.144444745829042688979198345693869549E-33), 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+0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, -0.385185988877447170611195588516985464E-33), (-0.481482486096808963263994485646231830E-33, +0.481482486096808963263994485646231830E-34), (-0.385185988877447170611195588516985464E-33, -0.240741243048404481631997242823115915E-34), (-0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (-0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33), (-0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33), (-0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33), (+0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-33), (-0.962964972193617926527988971292463659E-34, -0.337037740267766274284796139952362281E-33), (-0.288889491658085377958396691387739098E-33, -0.168518870133883137142398069976181140E-33), (-0.962964972193617926527988971292463659E-33, -0.349074802420186498366396002093518076E-33), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-33), (-0.385185988877447170611195588516985464E-33, -0.433334237487128066937595037081608647E-33)
480reltol = sqrt(epsilon(1._TKG))
481reltol
482+0.138777878078144567552953958511352539E-16
483isClose(data, atad(1:size(data)), reltol = reltol)
484T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
485call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
486
487lenData = getUnifRand(5, 100)
488lenData
489+29
490data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
491data
492+1.17059779, +1.81082726, +1.03938627, +1.75916851, +1.38391018, +1.73342395, +1.08356357, +1.75203371, +1.12692904, +1.26610756, +1.16000748, +1.49757719, +1.65446389, +1.06020188, +1.42852533, +1.02963674, +1.50979221, +1.58562613, +1.38907504, +1.19447243, +1.33196139, +1.10628104, +1.53159666, +1.32571673, +1.59996533, +1.61238956, +1.91850650, +1.38124907, +1.27372599
493
494atad = getFFTR(getFFTF(data))
495atad = atad * 2 / size(atad)
496atad
497+1.17059779, +1.81082737, +1.03938639, +1.75916851, +1.38391042, +1.73342395, +1.08356357, +1.75203347, +1.12692904, +1.26610768, +1.16000760, +1.49757719, +1.65446413, +1.06020212, +1.42852581, +1.02963662, +1.50979233, +1.58562624, +1.38907516, +1.19447243, +1.33196163, +1.10628104, +1.53159690, +1.32571626, +1.59996557, +1.61238968, +1.91850650, +1.38124895, +1.27372587, +0.298023224E-6, +0.238418579E-6, +0.119209290E-6
498reltol = sqrt(epsilon(1._TKG))
499reltol
500+0.345266977E-3
501isClose(data, atad(1:size(data)), reltol = reltol)
502T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
503call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
504
505lenData = getUnifRand(5, 100)
506lenData
507+64
508data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
509data
510+1.8783057163674599, +1.2373462001185236, +1.3899394386267632, +1.4099222713222348, +1.7886672443153340, +1.3032669453111183, +1.0648980797355678, +1.4342242310390274, +1.0160640032178654, +1.8431225056886174, +1.9817255297297363, +1.4950372996395291, +1.1459396079254474, +1.9417493119970668, +1.0354401097066446, +1.8154637129204239, +1.9582954569469555, +1.9534761852829172, +1.3004209352615628, +1.5615507747483608, +1.1377757549619099, +1.4759879213233624, +1.2095998984003900, +1.9985925535314308, +1.5430782754410257, +1.6924398357565553, +1.4840282052786531, +1.5893283446487123, +1.7453608910963214, +1.8836398041297380, +1.3868148415130750, +1.7370312554008918, +1.0962713674394100, +1.8691619532190868, +1.4234600084511793, +1.6348812496402183, +1.9627437656781987, +1.4383783848742249, +1.3231774598578976, +1.2548974444755290, +1.5554822114354914, +1.3963294632033749, +1.9789844026376655, +1.0052328632277800, +1.7889267439153489, +1.6279893341164486, +1.2446668956172537, +1.3046249758259081, +1.7526229279348817, +1.1883804867600940, +1.7942744463932505, +1.4397918682364961, +1.9520958902071088, +1.3054927254801036, +1.9681721556663669, +1.5149240022650776, +1.1817559794666503, +1.1322274248393029, +1.3935283367911446, +1.3848879845912716, +1.3623077195206976, +1.2374418221944845, +1.5029930535592686, +1.6816437060908229
511
512atad = getFFTR(getFFTF(data))
513atad = atad * 2 / size(atad)
514atad
515+1.8783057163674601, +1.2373462001185234, +1.3899394386267629, +1.4099222713222344, +1.7886672443153342, +1.3032669453111183, +1.0648980797355683, +1.4342242310390274, +1.0160640032178656, +1.8431225056886171, +1.9817255297297360, +1.4950372996395287, +1.1459396079254476, +1.9417493119970672, +1.0354401097066448, +1.8154637129204234, +1.9582954569469555, +1.9534761852829168, +1.3004209352615628, +1.5615507747483603, +1.1377757549619101, +1.4759879213233624, +1.2095998984003904, +1.9985925535314308, +1.5430782754410257, +1.6924398357565551, +1.4840282052786533, +1.5893283446487119, +1.7453608910963214, +1.8836398041297380, +1.3868148415130750, +1.7370312554008915, +1.0962713674394102, +1.8691619532190866, +1.4234600084511793, +1.6348812496402179, +1.9627437656781990, +1.4383783848742249, +1.3231774598578983, +1.2548974444755290, +1.5554822114354918, +1.3963294632033747, +1.9789844026376655, +1.0052328632277798, +1.7889267439153489, +1.6279893341164493, +1.2446668956172540, +1.3046249758259081, +1.7526229279348819, +1.1883804867600936, +1.7942744463932505, +1.4397918682364959, +1.9520958902071091, +1.3054927254801036, +1.9681721556663669, +1.5149240022650776, +1.1817559794666506, +1.1322274248393029, +1.3935283367911449, +1.3848879845912712, +1.3623077195206976, +1.2374418221944850, +1.5029930535592686, +1.6816437060908229
516reltol = sqrt(epsilon(1._TKG))
517reltol
518+0.14901161193847656E-7
519isClose(data, atad(1:size(data)), reltol = reltol)
520T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T
521call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
522
523lenData = getUnifRand(5, 100)
524lenData
525+10
526data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)
527data
528+1.44135000361061158890920161604215639, +1.79257187339262464084529364528518385, +1.98618507103172880561208268338735246, +1.95514561929824986586956645612245747, +1.56846368458419403159935534528140963, +1.92104874366112994750665868120669857, +1.73985963421266429198040130440949784, +1.27987154248227707784756844401107612, +1.10950992529754106154068876559459901, +1.18226759744443672140992596084809230
529
530atad = getFFTR(getFFTF(data))
531atad = atad * 2 / size(atad)
532atad
533+1.44135000361061158890920161604215639, +1.79257187339262464084529364528518405, +1.98618507103172880561208268338735246, +1.95514561929824986586956645612245766, +1.56846368458419403159935534528140963, +1.92104874366112994750665868120669857, +1.73985963421266429198040130440949784, +1.27987154248227707784756844401107593, +1.10950992529754106154068876559459901, +1.18226759744443672140992596084809230, +0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.385185988877447170611195588516985464E-33
534reltol = sqrt(epsilon(1._TKG))
535reltol
536+0.138777878078144567552953958511352539E-16
537isClose(data, atad(1:size(data)), reltol = reltol)
538T, T, T, T, T, T, T, T, T, T
539call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))
540
541
Test:
test_pm_fftnr


Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

  1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
  2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright
Computational Data Science Lab
Author:
Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 611 of file pm_fftnr.F90.

The documentation for this interface was generated from the following file: